Maximum Linear Forest of Graphs Resulting from Some Binary Operations

Abstract

For a connected nontrivial graph G, the maximum linear forest of G is the linear forest having maximum number of edges. The number of edges in a maximum linear forest is denoted by \(\ell\)`(G).  In this paper we determine the maximum linear forest of the join and union of nontrivial connected graphs G and H , denoted by G + H and G \(\cup\) H , respectively.