Tree Cover of the Join and the Corona of Graphs

article distributed under the Creative Commons Attribution License, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let G be a graph and TG = {G1, G2, G3,..., Gk} be a collection of subgraphs of G where Gi is a subtree of G for every i ∈ {1, 2,..., k}. If for every edge e ∈ E(G), there exists Gi ∈ TG such that e ∈ E(Gi), then TG is a tree cover of G. The tree covering number of G is the minimum cardinality among the tree covers of G. In this paper, we establish some bounds for the tree covering numbers of the join and the corona of two vertex-disjoint graphs