Year: 2026
Type: article
Abstract: Let [Formula: see text] be an undirected graph. The set [Formula: see text] is called the closed neighborhood of a vertex [Formula: see text] and for an edge [Formula: see text], the closed neighborhood of [Formula: see text] is the set [Formula: see text], which is denoted by [Formula: see text] or [Formula: see text]. A set [Formula: see text] is called liar’s vertex-edge dominating set of a graph [Formula: see text] if for every [Formula: see text], [Formula: see text] and for every pair of distinct edges [Formula: see text], [Formula: see text]. The notion of liar’s vertex-edge domination arises naturally from some applications in communication networks. Given a graph [Formula: see text], the Minimum Liar’s Vertex-Edge Domination Problem (MinLVEDP) asks to find a liar’s vertex-edge dominating set of [Formula: see text] of minimum cardinality. In this paper, we study this problem from an algorithmic point of view. We design two linear time algorithms for MinLVEDP in block graphs and proper interval graphs, respectively. On the negative side, we show that the decision version of liar’s vertex-edge domination problem is NP-complete for undirected path graphs.
Authors: Debojyoti Bhattacharya, Subhabrata Paul
Institution: Indian Institute of Technology Patna
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415348240