Triangle‐free equimatchable graphs

A graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. provided a characterization graphs with girth at least 5. In this paper, we extend result by providing complete structural 4, that is, no triangle, identifying triangle-free families. Our also extends given Akbari al., which proves only connected r-regular are C 5 , 7 and K r where positive integer. Given nonbipartite graph, our implies linear time recognition algorithm for graphs.