Radio mean D-distance labeling of some graphs
Publisher ijmra.us UGC Approved
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
A Radio Mean D-distance labeling of a connected graph G is an injective map f from the vertex set V(G) to ℕ such that for two distinct vertices u and v of G, d D (u, v) + í µí± í µí±¢ +í µí±(í µí±£) 2 ≥ 1 + diam D (G), where d D (u, v) denotes the D-distance between u and v and diam D (G) denotes the D-diameter of G. The radio mean D-distance number of f, rmn D (f) is the maximum label assigned to any vertex of G. The radio mean D-distance number of G, rmn D (G) is the minimum value of rmn D (f) taken over all radio mean D-distance labeling f of G. In this paper we find the radio mean D-distance number of some well known graphs.
Related papers
On Radio Mean D-Distance Number of Graph Obtained from Graph Operation
International Journal of Mathematics Trends and Technology, 2018
A Radio Mean D-distance labeling of a connected graph G is an injective map f from the vertex set V(G) to ℕ such that for two distinct vertices u and v of G, d D (u, v) + + () 2 ≥ 1 + diam D (G), where d D (u, v) denotes the D-distance between u and v and diam D (G) denotes the D-diameter of G. The radio mean Ddistance number of f, rmn D (f) is the maximum label assigned to any vertex of G. The radio mean D-distance number of G, rmn D (G) is the minimum value of rmn D (f) taken over all radio mean D-distance labeling f of G. In this paper we find the radio mean D-distance number of graph obtained from graph operation.
Radio D-distance number of some graphs
If u, v are vertices of a connected graph G the D-length of a connected u-v path s is defined as ℓ D s = ℓ(s) + deg (v) + deg (u) + deg (í µí±¤) where the sum runs over all intermediate vertices w of s and ℓ (s) is the length of the path. The D-distance d D (u, v) between two vertices u , v of a connected graph G is defined a d D (u, v) = min ℓ D (s) where the minimum is taken overall u-v paths s in G. In other words, d D (u, v) = min ℓ (s) + deg(v) + deg(u) + deg(í µí±¤) where the sum runs over all intermediate vertices w in s and minimum is taken over all u-v paths s in G. Radio D-distance coloring is a function í µí± : V(G) → ℕ ∪ 0 such that d D (u, v) + í µí± í µí±¢ − í µí±(í µí±£) ≥ diam D (G) + 1, where diam D (G) is the D-distance diameter of G. A D-distance radio coloring number of f is the maximum color assigned to any vertex of G. It is denoted by rn D (í µí±). In this paper we find the radio D-distance number of some well known graphs.
Radio labelings of distance graphs
Discrete Applied Mathematics, 2013
Distance-two labelings of graphs
European Journal of Combinatorics, 2003
For given positive integers j ≥ k, an L(j, k)-labeling of a graph G is a function f : V (G) → {0, 1, 2,. . .} such that | f (u) − f (v)| ≥ j when d G (u, v) = 1 and | f (u) − f (v)| ≥ k when d G (u, v) = 2. The L(j, k)-labeling number λ j,k (G) of G is defined as the minimum m such that there is an L(j, k)-labeling f of G with f (V (G)) ⊆ {0, 1, 2,. .. , m}. For a graph G of maximum degree ∆ ≥ 1 it is the case that λ j,k (G) ≥ j + (∆ − 1)k. The purpose of this paper is to study the structures of graphs G with maximum degree ∆ ≥ 1 and λ j,k (G) = j + (∆ − 1)k.
On L(d,1)-labelings of graphs
Discrete Mathematics, 2000
Given a graph G and a positive integer d, an L(d; 1)-labeling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then |f(u) − f(v)|¿d; if u and v are not adjacent but there is a two-edge path between them, then |f(u) − f(v)|¿1. The L(d; 1)-number of G, d (G), is deÿned as the minimum m such that there is an L(d; 1)-labeling f of G with f(V) ⊆{0; 1; 2; : : : ; m}. Motivated by the channel assignment problem introduced by Hale (Proc. IEEE 68 (1980) 1497-1514), the L(2; 1)-labeling and the L(1; 1)-labeling (as d = 2 and 1, respectively) have been studied extensively in the past decade. This article extends the study to all positive integers d. We prove that d (G)6 2 + (d − 1) for any graph G with maximum degree. Di erent lower and upper bounds of d (G) for some families of graphs including trees and chordal graphs are presented. In particular, we show that the lower and the upper bounds for trees are both attainable, and the upper bound for chordal graphs can be improved for several subclasses of chordal graphs.
L(2, 1)-labellings of integer distance graphs
2008
Let D be a set of positive integers. The (integer) distance graph G(Z, D) with distance set D is the graph with vertex set Z, in which two vertices x, y are adjacent if and only if |x − y| ∈ D. An L(2, 1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that labels of any two adjacent vertices differ by at least 2, and labels of any two vertices that are at distance two apart are distinct. The minimum range of labels over all L(2, 1)-labellings of a graph G is called the L(2, 1)−labelling number, or simply the λ-number of G, and is denoted by λ(G). We use λ(D) to denote the λ-number of G(Z, D). In this paper, some bounds for λ(D) are established. It is also shown that distance graphs satisfy the conjecture λ(G) ≤ ∆ 2. We also use a periodic labelling and prove that there exists an algorithm to determine the labelling number for any distance graph with finite distance set. For some special distance sets D, better upper bounds for λ(D) are obtained. We shall also determine the exact values of λ(D) for some two element set D.
On Distance Irregular Labeling of Disconnected Graphs
Kragujevac Journal of Mathematics
A distance irregular k-labeling of a graph G is a function f : V (G) → {1, 2, . . . , k} such that the weights of all vertices are distinct. The weight of a vertex v, denoted by wt(v), is the sum of labels of all vertices adjacent to v (distance 1 from v), that is, wt(v) = P u∈N(v) f(u). If the graph G admits a distance irregular labeling then G is called a distance irregular graph. The distance irregularity strength of G is the minimum k for which G has a distance irregular k-labeling and is denoted by dis(G). In this paper, we derive a new lower bound of distance irregularity strength for graphs with t pendant vertices. We also determine the distance irregularity strength of some families of disconnected graphs namely disjoint union of paths, suns, helms and friendships.
Distance Two labeling for Multi-Storey Graphs
International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks, 2010
An L (2, 1)-labeling of a graph G (also called distance two labeling) is a function f from the vertex set V (G) to the non negative integers {0,1,…, k }such that |f(x)-f(y)| ≥2 if d(x, y) =1 and | f(x)-f(y)| ≥1 if d(x, y) =2. The L (2, 1)-labeling number λ (G) or span of G is the smallest k such that there is a f with max {f (v) : vє V(G)}= k. In this paper we introduce a new type of graph called multi-storey graph. The distance two labeling of multi-storey of path, cycle, Star graph, Grid, Planar graph with maximal edges and its span value is determined. Further maximum upper bound span value for Multi-storey of simple graph are discussed.
d-Lucky Labeling of Graphs
Procedia Computer Science, 2015
Let l : V (G) →N be a labeling of the vertices of a graph G by positive integers. Define , where d(u) denotes the degree of u and N(u) denotes the open neighborhood of u. In this paper we introduce a new labeling called d-lucky labeling and study the same as a vertex coloring problem. We define a labeling l as d-lucky if , for every pair of adjacent vertices u and v in G. The d-lucky number of a graph G, denoted by dl (G), is the least positive k such that G has a d-lucky labeling with as the set of labels. We obtain dl (G) = 2 for hypercube network, butterfly network, benes network, mesh network, hypertree and X-tree.
Related topics
Related papers
Graceful distance labeling for some particular graphs
2021
In this paper, we define a new type of labeling for graphs which we call graceful distance labeling (GDL). An injective mapping f from the vertex set V (G) into the set of non-negative integers such that the absolute difference of labels of vertices u and v is greater than or equal to distance between them i.e. | f (u)− f (v)| ≥ d(u,v) where d(u,v) denotes the distance between the vertices u and v in G. The graceful distance labeling number (GDLN), λd(G) of G is the minimum k where G has a graceful distance labeling f with k being the absolute difference between the largest and smallest image points of f i.e. λd(G) = mink, where k = max | f (u)− f (v)|. In this paper, we find the values of k for different graphs.
Distance magic labelings of graphs
2003
As a natural extension of previously defined graph labelings, we introduce in this paper a new magic labeling whose evaluation is based on the neighbourhood of a vertex. We define a 1-vertex-magic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2,. .. , v with the property that there is a constant k such that at any vertex x, y∈N (x) f (y) = k, where N (x) is the set of vertices adjacent to x. We completely solve the existence problem of 1-vertex-magic vertex labelings for all complete bipartite, tripartite and regular multipartite graphs, and obtain some non-existence results for other natural families of graphs.
On distance labelings of 2-regular graphs
Electronic Journal of Graph Theory and Applications, 2021
Let G be a graph with |V (G)| vertices and ψ : V (G) −→ {1, 2, 3, • • • , |V (G)|} be a bijective function. The weight of a vertex v ∈ V (G) under ψ is w ψ (v) = u∈N (v) ψ(u). The function ψ is called a distance magic labeling of G, if w ψ (v) is a constant for every v ∈ V (G). The function ψ is called an (a, d)-distance antimagic labeling of G, if the set of vertex weights is a, a + d, a + 2d,. .. , a + (|V (G)| − 1)d. A graph that admits a distance magic (resp. an (a, d)distance antimagic) labeling is called distance magic (resp. (a, d)-distance antimagic). In this paper, we characterize distance magic 2-regular graphs and (a, d)-distance antimagic some classes of 2-regular graphs.
Radio Labelings of Lexicographic Product of Some Graphs
Journal of Mathematics, 2021
Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping ℘: V(G) ⟶ Z + satisfying the condition |℘(μ) − ℘(μ′)| ≥ diam(G) + 1 − d(μ, μ′): μ, μ′ ∈ V(G) for any pair of vertices μ, μ′ in G. e span of labeling ℘ is the largest number that ℘ assigns to a vertex of a graph. Radio number of G, denoted by rn(G), is the minimum span taken over all radio labelings of G. In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.
The edge span of distance two labelings of graphs
TAIWANESE JOURNAL OF MATHEMATICS
The radio channel assignment problem can be cast as a graph coloring problem. Vertices correspond to transmitter locations and their labels (colors) to radio channels. The assignment of frequencies to each transmitter (vertex) must avoid interference which depends on the seperation each pair of vertices has. Two levels of interference are assumed in the problem we are concerned. Based on this channel assignment problem, we proposed a graph labelling problem which has two constraints instead of one. We consider the question of finding the minimum edge of this labelling. Several classes of graphs including one that is important to a telecommunication problem have been studied.
On the $k$-distant total labeling of graphs
Malaya Journal of Matematik
A labeling of a graph is a mapping that maps some set of graph elements to a set of numbers. In this paper, two new variations of labeling named k-distant edge total labeling and k-distant vertex total labeling are introduced. Moreover, the study of two new graph parameters, called k-distant edge chromatic number (γ kd) and k-distant vertex chromatic number (γ kd) related this labeling are initiated. The k-distant vertex total labeling for paths, cycles, complete graphs, stars, bi-stars and friendship graphs are studied and the value of the parameter γ kd determined for these graph classes. Then k-distant edge total labeling for paths, cycles and stars are studied. Also, an upper bound of γ kd and a lower bound of γ kd are presented for general graphs.
On -labelings of graphs
Discrete Mathematics, 2000
Given a graph G and a positive integer d, an L(d; 1)-labeling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then |f(u) − f(v)|¿d; if u and v are not adjacent but there is a two-edge path between them, then
Multilevel Bandwidth and Radio Labelings of Graphs
Lecture Notes in Computer Science, 2008
This paper introduces a generalization of the graph bandwidth parameter: for a graph G and an integer k ≤ diam(G), the k-level bandwidth B k (G) of G is defined by B k (G) = minγ max{|γ(x)−γ(y)|−d(x, y)+1 : x, y ∈ V (G), d(x, y) ≤ k}, the minimum being taken among all proper numberings γ of the vertices of G. We present general bounds on B k (G) along with more specific results for k = 2 and the exact value for k = diam(G). We also exhibit relations between the k-level bandwidth and radio k-labelings of graphs from which we derive a upper bound for the radio number of an arbitrary graph.
Distance-two labellings of Hamming graphs
Discrete Applied Mathematics, 2009
d, 1)-total labeling of graphs with a given maximum average degree
Journal of Graph Theory, 2006
The (d,1)-total number of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G so that no two adjacent vertices have the same color, no two incident edges have the same color, and the distance between the color of a vertex and its incident edges is at least d. In this paper, we prove that for connected graphs with a given maximum average degree. © 2005 Wiley Periodicals, Inc. J Graph Theory
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.