On well (edge) dominated and equimatchable strong product graphs

TL;DR

This paper characterizes well-edge-dominated and equimatchable properties in strong product graphs, providing full classifications and identifying families of graphs with these properties preserved under strong products.

Contribution

It offers a complete characterization of well-edge-dominated and equimatchable strong product graphs and identifies a large family of graphs maintaining these properties.

Findings

Full characterization of well-edge-dominated strong product graphs.

Complete classification of equimatchable strong product graphs.

Identification of graph families with property preservation under strong products.

Abstract

A graph is well-(edge-)dominated if every minimal (edge) dominating set is minimum. A graph is equimatchable if every maximal matching is maximum. We study these concepts on strong product graphs. We fully characterize well-edge-dominated and equimatchable strong product graphs of nontrivial graphs, and identify a large family of graphs whose strong products with any well-dominated graph are well-dominated.