Some family of distance pattern distinguishing graphs and realization results. (18th May 2020) - Ananthakumar, R.
Abstract: Let G = ( V, E ) be a connected graph and let M ⊆ V . For each u ∊ V the set fM ( u ) = { d ( u, v ) : v ∊ M } is called the distance pattern of u with respect to the set M . If fM is injective, then the set M is called a distance pattern distinguishing set ( DPD -set) of G . If G admits a DPD -set, then G is called a DPD -graph. The minimum cardinality of a DPD -set in a DPD -graph G is the DPD -number of G and it is denoted by ρ ( G ). In this paper we present several fundamental results on these concepts and some family of graphs which admits DPD -set. We also investigate the relation between the DPD -number and the metric dimension of graphs and other graph theoretic parameters.