DOMINATING CYCLE OF n-CONNECTED GRAPH
A cycle C of a graph G is called a dominating cycle if every vertex of G is adjacent to at least one vertex of C. In this paper, we obtain the following result: let be an integer. Let H be a subgraph of n-connected graph G. Then either H can be dominated by a cycle in G, or there exists a cycle C of G such that where the distance between v and C in G is at most Let T be a tree. The set of leaves of T is denoted by The subtree is called the stem of T. By using above result, we give two sufficient conditions for an n-connected graph to have a spanning tree whose stem has a few of leaves.
dominating cycle, 4-stable set, spanning tree, stem, leaf.