Covering codes of a graph associated to a finite vector space

Abstract

UDC 512.5 In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das [Commun. Algebra, <strong>44</strong>, 3918 – 3926 (2016)], such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-dominating sets and identifying codes, which are closely related concepts for this purpose. We find the location-domination number and the identifying number of the graph and study the exchange property for locating-dominating sets and identifying codes.

Automorphism Group and Other Properties of Zero Component Graph over a Vector Space

“…When the base field F is finite, Das [5] considered the clique number, edge connectivity, and chromatic number of Γ c (V) and showed that Γ c (V) is Hamiltonian, but not Eulerian. Murtaza et al [6] considered two parameters, called the locating-dominating number and identifying number, of Γ c (V). Also, the nonzero component union graph Γ u (V) of V has V * as its vertex set, but two vertices α, β ∈ V * are adjacent if and only if〈S A (α), S A (β)〉 � V, where 〈S〉 stands for the subspace of V generated by a subset S⊆V.…”