2011•Journal of Southern Vocational EducationRequires access
Edge Critical Graph
Lin Yu-qing
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Abstract
We defined edge critical graph in the paper.We study the question and obtain:1) if G is △(G) edge critical graph,then G is star graph S△(G);2) if G is △(G)+1 edge critical graph,then G is not cut edge;3) if G is △(G)+1 edge critical graph,then at any edge uv of G there are d(u)+ d(v)≥△(G)+2;4)if G is simple conneted graph of △(G)=3,ν(G)is even,and χ/(G)= △(G)+1,then there is a vertex of G,and χ/(G-v)= χ/(G)= △(G)+1 is ture.We give the conjecture:if G is △(G)+1 edge critical graph,then ν(G) is odd.;and obtain the conclusion which this conjecture and other conjecture:as G is a simple graph,and ν(G) is even,and χ/(G)=△(G)+1,then there is a vertex of G,and χ/(G-v)= χ/(G)= △(G)+1 is ture.,is of equal value.