On the total irredundant number of non-regular graphs
Hanyuan Deng · 2004
Let G=(V,E) be an undirected graph,a set S of vertices in the graph G is called a total irredundant set if,for every vertex v in G,v or one of its neighbors has no neighbor in S-{v}.The total irredundance number ir t(G) is the minimum cardinality of any total irredundanct set,while the upper total irredundance number IR t(G) is the maximal cardinality of any such set.In this paper,we give a upper bound of IR t(G) for a non-regular connected graph G in terms of maximum degree Δ(G),minimum degree δ(G) and its order n.We show that IR t(G)n1+(Δ+1)δ(Δ-1)Δ and the bound is sharp.