A Sufficient Condition on I(G)=γ(G) for 3-γ-critical Graph
Chun Wang · Mathematica Applicata · 2000
Sumner and Blitch defined a graph G to be k γ critical if γ(G)=k and γ(G+uv)=k-1 for each pair u,v of nonadjacent vertices of G. And conjecture that γ(G)=i(G) for 3 γ critical graph. Henning Oellermann and Swart defined a graph to be k (γ,d) critical if γ(G)=k and γ(G+uv)=k-1 for each pair u,v of nonadjacent vertices of G that are at distance at most d apart. And conjecture: if G is a connected 3 (γ,2) critical graph, then γ(G)=i(G). In this paper we prove that a sufficient condition on γ(G)=i(G) for 3 γ critical graph.