Papers by andrea semanicova
Fundamenta Informaticae
Let G = (V, E) be a finite simple undirected graph without K2 components. A bijection f : E → {1,... more Let G = (V, E) be a finite simple undirected graph without K2 components. A bijection f : E → {1, 2, ⋯, |E|} is called a local antimagic labeling if for any two adjacent vertices u and v, they have different vertex sums, i.e., w(u) ≠ w(v), where the vertex sum w(u) = ∑e∈E(u) f(e), and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color (vertex sum) w(v). The local antimagic chromatic number χla(G) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. It was conjectured [6] that for every tree T the local antimagic chromatic number l + 1 ≤ χla(T) ≤ l + 2, where l is the number of leaves of T. In this article we verify the above conjecture for complete full t-ary trees, for t ≥ 2. A complete full t-ary tree is a rooted tree in which all nodes have exactly t children except leaves and every leaf is of the same depth. In particular we obtain ...
Electronic Journal of Graph Theory and Applications
A simple graph G(V, E) admits an H-covering if every edge in G belongs to a subgraph of G isomorp... more A simple graph G(V, E) admits an H-covering if every edge in G belongs to a subgraph of G isomorphic to H. In this case, G is called H-magic if there exists a bijective function f : V ∪ E → {1, 2,. .. , |V | + |E|}, such that for every subgraph H ′ of G isomorphic to H, wt f (H ′) = v∈V (H ′) f (v) + e∈E(H ′) f (e) is constant. Moreover, G is called H-supermagic if f : V (G) → {1, 2,. .. , |V |}. This paper generalizes the previous labeling by introducing the (F, H)-sim-(super) magic labeling. A graph admitting an F-covering and an H-covering is called (F, H)-sim-(super) magic if there exists a function f that is F-(super)magic and H-(super)magic at the same time. We consider such labelings for two product graphs: the join product and the Cartesian product. In particular, we establish a sufficient condition for the join product G + H to be (K 2 + H, 2K 2 + H)sim-supermagic and show that the Cartesian product G × K 2 is (C 4 , H)-sim-supermagic, for H isomorphic to a ladder or an even cycle. Moreover, we also present a connection between an α-labeling of a tree T and a (C 4 , C 6)-sim-supermagic labeling of the Cartesian product T × K 2 .
Symmetry
A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defi... more A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the remainder of the division of the sum of end vertex labels by modulo |E(G)|. The modular edge irregularity strength of a graph is known as the maximal vertex label k, minimized over all modular edge irregular k-labelings of the graph. In this paper we describe labeling schemes with symmetrical distribution of even and odd edge weights and investigate the existence of (modular) edge irregular labelings of joins of paths and cycles with isolated vertices. We estimate the bounds of the (modular) edge irregularity strength for the join graphs Pn+Km¯ and Cn+Km¯ and determine the corresponding exact value of the (modular) edge irregularity strength for some fan graphs and wheel graphs in order to prove the sharpness of the presented bounds.
International Symposium on Algorithms and Computation, Jul 1, 2013
In this paper we construct antimagic labelings of the regular complete multipartite graphs and we... more In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.
Mathematics, 2021
An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is... more An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is a local antimagic labeling if the vertex-weights are distinct for every pair of neighboring vertices, where a vertex-weight is the sum of labels of all edges incident with that vertex. Any local antimagic labeling induces a proper vertex coloring of G where the color of a vertex is its vertex-weight. This naturally leads to the concept of a local antimagic chromatic number. The local antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G. In this paper, we estimate the bounds of the local antimagic chromatic number for disjoint union of multiple copies of a graph.
Australas. J Comb., 2017
A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomo... more A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs ∗ Corresponding author. P. JAYANTHI ET AL. /AUSTRALAS. J. COMBIN. 67 (1) (2017), 46–64 47 H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithmetic progression a, a + d, a + 2d, . . . , a + (t − 1)d where a is the first term, d is the common difference and t is the number of subgraphs of G isomorphic to H . Such a labeling is called super if f(V ) = {1, 2, . . . , |V |}. This paper deals with some results on anti-balanced sets and we show the existence of super (a, d)-cycle-antimagic labelings of fans and some square graphs.
Mathematics, 2021
Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclus... more Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x,y∈V(G) their weights are distinct, where the weight of a vertex x∈V(G) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for d=1 and determine the precise values of the corresponding graph invariant for certain families of graphs.
Australas. J Comb., 2017
A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph... more A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. This paper is devoted to studying the existence of super (a, d)-Hantimagic labelings for fans when subgraphs H are cycles.
arXiv: Combinatorics, 2017
Let $D$ be a digraph, possibly with loops. A queen labeling of $D$ is a bijective function $l:V(G... more Let $D$ be a digraph, possibly with loops. A queen labeling of $D$ is a bijective function $l:V(G)\longrightarrow \{1,2,\ldots,|V(G)|\}$ such that, for every pair of arcs in $E(D)$, namely $(u,v)$ and $(u',v')$ we have (i) $l(u)+l(v)\neq l(u')+l(v')$ and (ii) $l(v)-l(u)\neq l(v')-l(u')$. Similarly, if the two conditions are satisfied modulo $n=|V(G)|$, we define a modular queen labeling. There is a bijection between (modular) queen labelings of $1$-regular digraphs and the solutions of the (modular) $n$-queens problem. The $\otimes_h$-product was introduced in 2008 as a generalization of the Kronecker product and since then, many relations among labelings have been established using the $\otimes_h$-product and some particular families of graphs. In this paper, we study some families of $1$-regular digraphs that admit (modular) queen labelings and present a new construction concerning to the (modular) $n$-queens problem in terms of the $\otimes_h$-product, whi...
Complexity, 2021
In this work, we introduce a new topological index called a general power sum-connectivity index ... more In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α , where d u and d v represent the degree of vertices u and v , respectively, and α ≥ 1 . A connected graph G is called a k -generalized quasi-tree if there exists a subset V k ⊂ V G of cardinality k such that the graph G − V k is a tree but for any subset V k − 1 ⊂ V G of cardinality k − 1 , the graph G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.
AKCE International Journal of Graphs and Combinatorics, 2020
Let G ¼ ðV, EÞ be a finite simple graph with p vertices and q edges. A decomposition of a graph G... more Let G ¼ ðV, EÞ be a finite simple graph with p vertices and q edges. A decomposition of a graph G into isomorphic copies of a graph H is called (a, d)-H-antimagic if there is a bijection f : V [ E ! f1, 2, :::, p þ qg such that for all subgraphs H 0 isomorphic to H in the decomposition of G, the sum of the labels of all the edges and vertices belonging to H 0 constitutes an arithmetic progression with the initial term a and the common difference d. When f ðVÞ ¼ f1, 2, :::, pg, then G is said to be super (a, d)-H-antimagic and if d ¼ 0 then G is called H-supermagic. In the paper we examine the existence of such labelings for toroidal grids and toroidal triangulations.
Results in Mathematics, 2020
Let D be a digraph, possibly with loops. A queen labeling of D is a bijective function l : V (G) ... more Let D be a digraph, possibly with loops. A queen labeling of D is a bijective function l : V (G) −→ {1, 2,. .. , |V (G)|} such that, for every pair of arcs in E(D), namely (u, v) and (u ′ , v ′) we have (i) l(u) + l(v) = l(u ′) + l(v ′) and (ii) l(v) − l(u) = l(v ′) − l(u ′). Similarly, if the two conditions are satisfied modulo n = |V (G)|, we define a modular queen labeling. There is a bijection between (modular) queen labelings of 1-regular digraphs and the solutions of the (modular) n-queens problem. The ⊗ h-product was introduced in 2008 as a generalization of the Kronecker product and since then, many relations among labelings have been established using the ⊗ h-product and some particular families of graphs. In this paper, we study some families of 1-regular digraphs that admit (modular) queen labelings and present a new construction concerning to the (modular) n-queens problem in terms of the ⊗ h-product, which in some sense complements a previous result due to Pólya.
Hacettepe Journal of Mathematics and Statistics, 2019
A simple graph $G=(V,E)$ admits an~$H$-covering if every edge in $E$ belongs to at least one subg... more A simple graph $G=(V,E)$ admits an~$H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. The graph $G$ admitting an $H$-covering is $(a,d)$-$H$-antimagic if there exists a~bijection $f:V\cup E\to\{1,2,\cdots,|V|+|E|\}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H'$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e)$, form an~arithmetic progression with the initial term $a$ and the common difference $d$. Such a labeling is called {\it super} if the smallest possible labels appear on the vertices. In this paper we prove the existence of super $(a,d)$-$H$-antimagic labelings of fan graphs and ladders for $H$ isomorphic to a cycle.
ScienceAsia, 2018
The graph G is said to be H-magic if there exists a bijection ψ : V (G) ∪ E(G) → {1, 2,. .. , |V ... more The graph G is said to be H-magic if there exists a bijection ψ : V (G) ∪ E(G) → {1, 2,. .. , |V (G)| + |E(G)|} such that for every subgraph H of G isomorphic to H, the sum v∈V (H) ψ(v) + e∈E(H) ψ(e) is constant. Furthermore, G is said to be H-supermagic if ψ(V (G)) = {1, 2,. .. , |V (G)|}. In this paper, we study the cycle-supermagic labelling of a pumpkin graph and two classes of planar maps containing 8-sided and 4-sided faces or 6-sided and 4-sided faces, respectively.
TURKISH JOURNAL OF MATHEMATICS, 2018
A graph G = (V (G), E(G)) admits an H-covering if every edge in E belongs to a subgraph of G isom... more A graph G = (V (G), E(G)) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called (a, d)-H-antimagic if there is a bijection f : V (G) ∪ E(G) → {1, 2,. .. , |V (G)| + |E(G)|} such that, for all subgraphs H ′ of G isomorphic to H , the H-weights, wt f (H ′) = ∑ v∈V (H ′) f (v)+ ∑ e∈E(H ′) f (e), constitute an arithmetic progression with the initial term a and the common difference d. In this paper we provide some sufficient conditions for the Cartesian product of graphs to be H-antimagic. We use partitions subsets of integers for describing desired H-antimagic labelings.
Developments in Mathematics, 2019
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Hacettepe Journal of Mathematics and Statistics, 2018
A simple graph G = (V, E) admitting an H-covering is said to be (a, d)-H-antimagic if there exist... more A simple graph G = (V, E) admitting an H-covering is said to be (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2,. .. , |V | + |E|} such that, for all subgraphs H of G isomorphic to H, wt f (H) = v∈V (H) f (v) + e∈E(H) f (e), form an arithmetic progression a, a + d,. .. , a + (t − 1)d, where a is the first term, d is the common difference and t is the number of subgraphs in the H-covering. Then f is called an (a, d)-H-antimagic labeling. If f (V) = {1, 2,. .. , |V |}, then f is called super (a, d)-H-antimagic labeling. In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a starantimagic graph.
Acta Mechanica Slovaca, 2015
Let G = (V,E) be a finite simple graph with p vertices and q edges. An edge-covering of G is a fa... more Let G = (V,E) be a finite simple graph with p vertices and q edges. An edge-covering of G is a family of subgraphs H1,H2, ... ,Ht such that each edge of E(G) belongs to at least one of the subgraphs Hi, i=1,2, ... ,t. If every subgraph Hi is isomorphic to a given graph H, then the graph G admits an H-covering. Such a graph G is called (a,d)-H-antimagic if there is a bijection f: VjEg{1,2, ... ,p+q} such that for all subgraphs H′ of G isomorphic to H, the sum of the labels of all the edges and vertices belonging to H′ constitutes an arithmetic progression with the initial term a and the common difference d. When f(V)={1,2, ... ,p}, then G is said to be super (a,d)-H-antimagic; and if d = 0 then G is called H-supermagic. We will exhibit an operation on graphs which keeps super H-antimagic properties. We use a technique of partitioning sets of integers for the construction of the required labelings.
Open Mathematics, 2018
A simple graphG= (V,E) admits anH-covering, if every edge inE(G) belongs to a subgraph ofGisomorp... more A simple graphG= (V,E) admits anH-covering, if every edge inE(G) belongs to a subgraph ofGisomorphic toH. A graphGadmitting anH-covering is called an (a,d)-H-antimagic if there exists a bijective functionf:V(G) ∪E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphsH′ isomorphic toHthe sums ∑v∈V(H′)f(v) + ∑e∈E(H′)f(e) form an arithmetic sequence {a,a+d, …,a+ (t− 1)d}, wherea> 0 andd≥ 0 are integers andtis the number of all subgraphs ofGisomorphic toH. Moreover, if the vertices are labeled with numbers 1, 2, …, |V(G)| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a,d)-cycle-antimagic labeling for somed.
AKCE International Journal of Graphs and Combinatorics, 2016
Let G = (V, E) be a finite, simple and undirected graph. The edge-magic total or vertex-magic tot... more Let G = (V, E) be a finite, simple and undirected graph. The edge-magic total or vertex-magic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers {1, 2,. .. , |V (G)| + |E(G)|}, such that all the edge weights or vertex weights are equal to a constant, respectively. When all the edge weights or vertex weights are different then the labeling is called edge-antimagic or vertex-antimagic total, respectively. In this paper we provide some classes of graphs that are simultaneously super edge-magic total and super vertex-antimagic total, that is, graphs admitting labeling that has both properties at the same time. We show several results for fans, sun graphs, caterpillars and prisms. c
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Papers by andrea semanicova