Book ChapterDOI
On Prime Distance Labeling of Graphs
A. Parthiban,N. Gnanamalar David +1 more
- pp 238-241
TLDR
This paper derives certain general results concerning prime distance labeling of some cycle related graphs in the context of some graph operations, namely, power, fusion, duplication and vertex switching in cycle \(C_n\).Abstract:
A graph G is a prime distance graph if its vertices can be labeled with distinct integers in such a way that for any two adjacent vertices, the absolute difference of their labels is a prime number. It is known that cycles and bipartite graphs are prime distance graphs. In this paper we derive certain general results concerning prime distance labeling. We also investigate prime distance labeling of some cycle related graphs in the context of some graph operations, namely, power, fusion, duplication and vertex switching in cycle \(C_n\).read more
Citations
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Book ChapterDOI
Studying the Applications of Graph Labeling in Satellite Communication Through 2-Odd Labeling of Graphs
TL;DR: In this article , the authors studied the applications of graph theory in communication networks through the concept of 2-odd labeling in graphs, which assigns distinct integers to the nodes of a graph such that the positive difference of adjacent nodes is either 2 or an odd integer.
References
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Book
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TL;DR: In this article, the authors introduce the notion of linear constrains and apply them to the problem of computing the order of an integer and a primitive root for a given integer.
Journal ArticleDOI
Colouring the real line
TL;DR: The problem of colouring the real line so that the distance between like coloured numbers does not lie in some specified set D, called the distance set, is discussed.
Journal ArticleDOI
Colouring prime distance graphs
TL;DR: It is proved that ifD contains {2, 3} and also contains a pair of twin primes (one of which may be 3), then four colours are necessary, and numerous results regarding periodic colourings are obtained.
Journal ArticleDOI
Finite prime distance graphs and 2-odd graphs
TL;DR: It is proved that trees, cycles, and bipartite graphs are prime distance graphs, and that Dutch windmill graphs and paper mill graphs arePrime distance graphs if and only if the Twin Prime Conjecture and dePolignac’s Conjectures are true, respectively.