The Independent Edge Domination Topology Induced by Path Graphs
Jhon Neceir S. Ontulan *
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Cherry Mae R. Balingit
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
Let G = (V (G),E(G)) be a nonempty undirected graph. An independent edge dominating set is an independent set of edges which is also an edge dominating set of G. In the study of Ontulan and Balingit, they introduced a new approach of generating a unique topology from the family of independent edge dominating sets of G, this is called the independent edge domination topology on E(G), herein denoted as \(\tau^E_{ID}\) (G). This paper focuses on the independent edge domination topological space induced by the path graphs Pn, where n > 1. Moreover, some properties and characterizations of the independent edge dominating sets and the corresponding independent edge domination topology of path graphs are established.
Keywords: Independent edge domination topology, independent edge dominating set, independent edge, edge dominating set, path graphs, python program