Completely Independent Spanning Trees in Line Graphs

Completely independent spanning trees in a graph G are of such that for any two distinct vertices G, the paths between them pairwise edge-disjoint and internally vertex-disjoint. In this paper, we present tight lower bound on maximum number completely L(G), where L(G) denotes line G. Based new characterization with k trees, also show complete $$K_n$$ order $$n \ge 4$$ , there $$\lfloor \frac{n+1}{2} \rfloor $$ $$L(K_n)$$ is optimal, still exist obtained from by deleting vertex (respectively, induced path at most $$\frac{n}{2}$$ ) = or odd 5$$ even 6$$ ). Concerning connectivity moreover following, $$\delta (G)$$ minimum degree