The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and...The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and has been applied to studying network structures.In this paper we focus on the general sum-connectivity index which is a variant of the connectivity index.We characterize the tight upper and lower bounds of the largest eigenvalue of the general sum-connectivity matrix,as well as its spectral diameter.We show the corresponding extremal graphs.In addition,we show that the general sum-connectivity index is determined by the eigenvalues of the general sum-connectivity Laplacian matrix.展开更多
基金This work was supported by the Danish National Research Foundation and the National Science Foundation of China(No.61061130540)for the Sino-Danish Center for the Theory of Interactive Computation and by the Center for Research in Foundations of Electronic Markets(CFEM,supported by the Danish Strategic Research Council),within which this work was performedWe thank the anonymous reviewers for their thorough reviews and insightful comments,which helped us to improve the paper.
文摘The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and has been applied to studying network structures.In this paper we focus on the general sum-connectivity index which is a variant of the connectivity index.We characterize the tight upper and lower bounds of the largest eigenvalue of the general sum-connectivity matrix,as well as its spectral diameter.We show the corresponding extremal graphs.In addition,we show that the general sum-connectivity index is determined by the eigenvalues of the general sum-connectivity Laplacian matrix.
