On the Distance Pattern Distinguishing Number of a Graph

Sona Jose and Germina K. Augustine

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/328703

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:328703

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