Path Cover Number of Rook’s graph

Path Cover Number of Rook’s graph

The path cover number of graph G, is a set of induced paths of G that cover all vertices of graph G. The path cover number P(G) of graph G is the smallest positive integer k such that there are k vertex-disjoint path occurring as induced subgraphs of G that cover all the vertices of G. There are some relationships between P(G) and some other graph parameters such as minimum rank of graphs and zero forcing number, etc. Here we investigate the path cover number of Rook s graph and vertex-sum of two Rook s graphs.

The path cover number of graph G, is a set of induced paths of G that cover all vertices of graph G. The path cover number P(G) of graph G is the smallest positive integer k such that there are k vertex-disjoint path occurring as induced subgraphs of G that cover all the vertices of G. There are some relationships between P(G) and some other graph parameters such as minimum rank of graphs and zero forcing number, etc. Here we investigate the path cover number of Rook s graph and vertex-sum of two Rook s graphs.