Counting the Number of Star-Factors in Graphs

Qinglin Yu1,2
1 Department of Mathematics and Statistics University College of The Cariboo Kamloops, BC, Canada
2 Department of Mathematics and Statistics Simon Fraser University Burnaby, BC, Canada

Abstract

A star-factor of a graph \(G\) is a spanning subgraph of \(G\) such that each component of which is a star. In this paper, we study the structure of the graphs with a unique star-factor and obtain an upper bound on the mnumber of edges such graphs can have. We also investigate the number of star-factors in a regular graph.