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On the Distance Pattern Distinguishing Number of a Graph

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  • Sona Jose
  • Germina K. Augustine

Abstract

Let be a connected simple graph and let be a nonempty subset of . The -distance pattern of a vertex in is the set of all distances from to the vertices in . If the distance patterns of all vertices in are distinct, then the set is a distance pattern distinguishing set of . A graph 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.

Suggested Citation

  • Sona Jose & Germina K. Augustine, 2014. "On the Distance Pattern Distinguishing Number of a Graph," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, June.
    • Handle: RePEc:hin:jnljam:328703
    DOI: 10.1155/2014/328703
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