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2014 On the Distance Pattern Distinguishing Number of a Graph
Sona Jose, Germina K. Augustine
J. Appl. Math. 2014: 1-8 (2014). DOI: 10.1155/2014/328703

Abstract

Let G=(V,E) be a connected simple graph and let M be a nonempty subset of V. The M-distance pattern of a vertex u in G is the set of all distances from u to the vertices in M. If the distance patterns of all vertices in V are distinct, then the set M is a distance pattern distinguishing set of G. A graph G with a distance pattern distinguishing set is called a distance pattern distinguishing graph. Minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. This paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. Further, this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph.

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Sona Jose. Germina K. Augustine. "On the Distance Pattern Distinguishing Number of a Graph." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/328703

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131526
MathSciNet: MR3224363
Digital Object Identifier: 10.1155/2014/328703

Rights: Copyright © 2014 Hindawi

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