Edge open packing sets in graphs

¹ Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil 626126, Tamil Nadu, India
² Department of Mathematics, Thiagarajar College of Engineering, Madurai 625015, Tamil Nadu, India

^* Corresponding author: gaya320102012@gmail.com

Received: 17 August 2022
Accepted: 3 October 2022

Abstract

In a graph G = (V, E), two edges e₁ and e₂ are said to have a common edge if there exists an edge e ∈ E(G) different from e₁ and e₂ such that e joins a vertex of e₁ to a vertex of e₂ in G. That is, 〈e₁, e, e₂〉 is either P₄ or K₃ in G. A non-empty set D ⊆ E(G) is an edge open packing set of a graph G if no two edges of D have a common edge in G. The maximum cardinality of an edge open packing set is the edge open packing number of G and is denoted by ρ^o_e(G). In this paper, we initiate a study on this parameter.