Structural characterization of some family of local distance pattern distinguishing graphs. (17th November 2022)

• Record Type: Journal Article
• Authors: Ananthakumar, R.
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 25:Number 8(2022)
• Page Start: 2615
• Page End: 2627
• Publication Date: 2022-11-17
• Subjects: 05C12; LDPD-set -- LDPD-number; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2021.1891695
• Languages: English
• ISSNs: 0972-0529

Abstract

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.