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Local Distance Pattern Distinguishing Sets in Graphs

  • R. Anantha KumarEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Let G = (V, E) be a connected graph and W ⊆ V be a nonempty set. For each u ∈ V , the set fW(u) = {d(u, v) : v ∈ W} is called the distance pattern of u with respect to the set W. If fW(x) ≠ fW(y) for all xy ∈ E(G), then W is called a local distance pattern distinguishing set (or a LDPD-set in short) of G. The minimum cardinality of a LDPD-set in G, if it exists, is the LDPD-number of G and is denoted by ϱ(G). If G admits a LDPD-set, then G is called a LDPD-graph. In this paper we discuss the LDPD-number ϱ(G) of some family of graphs and the relation between ϱ(G) and other graph theoretic parameters. We characterized several family of graphs which admits LDPD-sets.

Keywords

LDPD-set LDPD-number Local metric set 

Notes

Acknowledgements

The author is thankful to Professor S. Arumugam for suggesting this problem. Also the author is very much grateful to the constant support of MEPCO Schlenk Engineering College (Autonomous), Sivakasi.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MEPCO Schlenk Engineering College (Autonomous)SivakasiIndia

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