ON THE USE OF COMPUTERS IN GRAPH LABELING : using generalized computer software developed by the ... more ON THE USE OF COMPUTERS IN GRAPH LABELING : using generalized computer software developed by the same author i.e., Auparajita Krishnaa in the year 2001 to analyze various aspects and patterns of different graph labelling schemes for different kinds of graphs which is not possible manually
International Journal of Mathematics Trends and Technology, 2016
This paper presents some applications of labelled graphs of different kinds of labellings alongwi... more This paper presents some applications of labelled graphs of different kinds of labellings alongwith various kinds of graphs serving as models for the applications.
Journal of Discrete Mathematical Sciences and Cryptography, 2016
Abstract This paper presents algorithms , formulas and proofs for antimagic labelings for some gr... more Abstract This paper presents algorithms , formulas and proofs for antimagic labelings for some graphs which are related in structure with helms. The labelings obtained are not only antimagic but also exhibit much regularity of patterns in the behaviour of the induced vertex labels.
Journal of Discrete Mathematical Sciences and Cryptography, 2013
( , ) ( ) ( ) g x y g x g y = * for all edges xy is injective. It seems that the graceful tree co... more ( , ) ( ) ( ) g x y g x g y = * for all edges xy is injective. It seems that the graceful tree conjecture expects a generalized result but for a generalized result the defi nition has to be a controlling factor in the sense that it could predict the behaviour of all the trees and trees being pictorial it is not possible. In this note we would look at the role of defi nitions in formulation of conjecture like the graceful tree conjecture. It is believed that a generalized result of the graceful tree conjecture is possible and this belief arises from a fi xed notion about equating the defi nition of trees with defi nitions in some other branches of mathematics. This note aims to shed light on the need of a rethinking of defi nitions of graph labellings of trees. Trees are defi ned as being acyclic and connected. But just being connected and acyclic does not put any limitation on shape, size and appearance or structure of the trees. Thus infi nite shapes of trees are possible. We know that labelling of any kind depends on the structure or shape of the graph, in this case a tree. There seems to be a perception rather a fi xed idea that defi nition of tree alone would predict and determine the behaviour of the infi nite kinds of trees not all of which can even be classifi ed being of infi nite shapes. This perception or fi xed idea overlooks the fact that graphs are pictorial and not fi xed structures or numbers, defi nition alone can not control or determine the shape and size of the tree and hence the existence of certain kind of labelling as well, which depends on shape and size of the
Journal of Discrete Mathematical Sciences and Cryptography, 2012
A simple graph G = (V, E) admits an H-covering if every edge in E belongs to at least one subgrap... 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 ∪ E → {1, 2,. .. , |V | + |E|} 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), 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. 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.
ON THE USE OF COMPUTERS IN GRAPH LABELING : using generalized computer software developed by the ... more ON THE USE OF COMPUTERS IN GRAPH LABELING : using generalized computer software developed by the same author i.e., Auparajita Krishnaa in the year 2001 to analyze various aspects and patterns of different graph labelling schemes for different kinds of graphs which is not possible manually
International Journal of Mathematics Trends and Technology, 2016
This paper presents some applications of labelled graphs of different kinds of labellings alongwi... more This paper presents some applications of labelled graphs of different kinds of labellings alongwith various kinds of graphs serving as models for the applications.
Journal of Discrete Mathematical Sciences and Cryptography, 2016
Abstract This paper presents algorithms , formulas and proofs for antimagic labelings for some gr... more Abstract This paper presents algorithms , formulas and proofs for antimagic labelings for some graphs which are related in structure with helms. The labelings obtained are not only antimagic but also exhibit much regularity of patterns in the behaviour of the induced vertex labels.
Journal of Discrete Mathematical Sciences and Cryptography, 2013
( , ) ( ) ( ) g x y g x g y = * for all edges xy is injective. It seems that the graceful tree co... more ( , ) ( ) ( ) g x y g x g y = * for all edges xy is injective. It seems that the graceful tree conjecture expects a generalized result but for a generalized result the defi nition has to be a controlling factor in the sense that it could predict the behaviour of all the trees and trees being pictorial it is not possible. In this note we would look at the role of defi nitions in formulation of conjecture like the graceful tree conjecture. It is believed that a generalized result of the graceful tree conjecture is possible and this belief arises from a fi xed notion about equating the defi nition of trees with defi nitions in some other branches of mathematics. This note aims to shed light on the need of a rethinking of defi nitions of graph labellings of trees. Trees are defi ned as being acyclic and connected. But just being connected and acyclic does not put any limitation on shape, size and appearance or structure of the trees. Thus infi nite shapes of trees are possible. We know that labelling of any kind depends on the structure or shape of the graph, in this case a tree. There seems to be a perception rather a fi xed idea that defi nition of tree alone would predict and determine the behaviour of the infi nite kinds of trees not all of which can even be classifi ed being of infi nite shapes. This perception or fi xed idea overlooks the fact that graphs are pictorial and not fi xed structures or numbers, defi nition alone can not control or determine the shape and size of the tree and hence the existence of certain kind of labelling as well, which depends on shape and size of the
Journal of Discrete Mathematical Sciences and Cryptography, 2012
A simple graph G = (V, E) admits an H-covering if every edge in E belongs to at least one subgrap... 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 ∪ E → {1, 2,. .. , |V | + |E|} 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), 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. 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.
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