2020/05/06 by Yaser Alizadeh, Alizadeh, Yaser, Sandi Klavžar +1
Mathematics · Materials Science · Computer Science · #Graph theory and applications #Graphene research and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2005.02635
The eccentric connectivity index of a graph G is \ξc(G) = \∑v \∈\nV(G)\ε(v)\deg(v), and the eccentric distance sum is \ξd(G) =\n\∑v \∈ V(G)\ε(v)D(v), where \ε(v) is the\neccentricity of v, and D(v) the sum of distances between v and the other\nvertices. A lower and an upper bound on \ξd(G) - \ξc(G) is given for an\narbitrary graph G. Regular graphs with diameter at most 2 and joins of\ncocktail-party graphs with complete graphs form the graphs that attain the two\nequalities, respectively. Sharp lower and upper bounds on \ξd(T) - \ξc(T)\nare given for arbitrary trees. Sharp lower and upper bounds on\n\ξd(G)+\ξc(G) for arbitrary graphs G are also given, and a sharp lower\nbound on \ξd(G) for graphs G with a given radius is proved.\n