The 1-nearly edge independence number of a graph
Year: 2026
Type: article
Abstract: Let $G = (V(G), E(G))$ be a graph. The maximum cardinality of a set $M_k \subseteq E(G)$ such that $M_k$ contains exactly $k$-pairs of adjacent edges of $G$ is called the $k$-nearly edge independence number of $G$, and is denoted by $α'_k(G)$. In this paper we study $α_1'(G)$. In particular, we prove a tight lower (resp. upper) bound on $α_1(G)$ if $G$ is a graph with given number of vertices. Furthermore, we present a characterisation of the general (resp. connected) graphs with given number of vertices and smallest $1$-nearly edge independence number. Lastly, we pose an open problem for further exploration of this study.
Source: Quaestiones Mathematicae
Author: Zekhaya B. Shozi
Institution: University of KwaZulu-Natal
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Funder: Inyuvesi Yakwazulu-Natali
OpenAlex ID: W4400667688