Structural characterization of some family of local distance pattern distinguishing graphs. (17th November 2022) - Ananthakumar, R.
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 ) ρ′ ( G ). If G admits a LDPD -set, then G is called a LDPD -graph. In this paper, we present the structure characteriation of some family of LDPD -graphs. Also, we discuss the LDPD -sets and LDPD -number in graph products.