Signed b-matchings and b-edge covers of strong product graphs

This is the authors' abstract. We don't add key points for this paper.

In this paper, we study the signed b-edge cover number and the signed b-matching number of a graph. Sharp bounds on these parameters of the strong product graphs are presented. We prove the existence of an analogue of Gallai's theorem relating maximum-size signed b-matchings and minimum-size signed b-edge covers for the complete graphs and complete bipartite graphs.