Edge-vertex domination on interval graphs

Abstract

For an undirected as well as connected graph [Formula: see text], a node point [Formula: see text] is edge-vertex dominated by an edge [Formula: see text] if [Formula: see text] is incident to [Formula: see text] or [Formula: see text] is incident to an adjacent edge of [Formula: see text]. A set [Formula: see text] is called an edge-vertex dominating set of [Formula: see text] if every node point of [Formula: see text] is edge-vertex dominated by at least one edge of [Formula: see text]. The minimum cardinality among all edge-vertex dominating sets is the edge-vertex domination number, symbolled by [Formula: see text]. Here, we propose an algorithm that runs in [Formula: see text]-time for determining a minimum-cardinality [Formula: see text] of interval graph with [Formula: see text] nodes. We also study some properties relating to the edge-vertex dominating set of interval graphs.