Graphs with Extremal Connectivity Index
نویسندگان
چکیده
Let G be a graph and δv the degree of its vertex v . The connectivity index of G is χ = ∑ (δu δv) −1/2 , with the summation ranging over all pairs of adjacent vertices of G . We offer a simple proof that (a) among n-vertex graphs without isolated vertices, the star has minimal χvalue, and (b) among n-vertex graphs, the graphs in which all components are regular of non–zero degree have maximal (mutually equal) χ-values. Both statements (a) and (b) are deduced using the same proof technique, based on linear programming. AMS Mathematics Subject Classification (2000): 05C35
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