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Distance-Based Graph Invariants Of Trees And The Harary Index, Stephan G. Wagner, Hua Wang, Xiao-Dong Zhang
Distance-Based Graph Invariants Of Trees And The Harary Index, Stephan G. Wagner, Hua Wang, Xiao-Dong Zhang
Department of Mathematical Sciences Faculty Publications
Introduced in 1947, the Wiener index W(T) = ∑{u,v}⊆V(T) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T) = ∑{u,v}⊆V(T) , introduced in 1993, can be considered as the 'reciprocal analogue' of the Wiener index. From recent studies, it is known that the extremal structures of the Harary index and the Wiener index coincide in many instances, i.e., the graphs that maximize the Wiener index minimize the Harary index and vice versa. In this …
Extremal Values Of Ratios: Distance Problems Vs. Subtree Problems In Trees, László A. Székely, Hua Wang
Extremal Values Of Ratios: Distance Problems Vs. Subtree Problems In Trees, László A. Székely, Hua Wang
Department of Mathematical Sciences Faculty Publications
The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems [Discrete Appl. Math. 155 (3) 2006, 374-385; Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80 (1997), 37-56] determined extremal values of σT(w)/σT(u), σT(w)/σT(v), σ(T)/σT(v), and σ(T)/σT(w), where T is a tree on n vertices, v is in the centroid of …
Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang
Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang
Department of Mathematical Sciences Faculty Publications
The degree distance of a graph G is D'(G)=(1/2)∑ni=1∑nj=1(di+dj)Li ,j, where di and dj are the degrees of vertices vi, vj ∈ V (G), and Li,j is the distance between them. The Wiener index is defined as W(G)=(1/2)∑ni=1 ∑nj-1Li, j. An elegant result (Gutman; Klein, Mihalic, Plavsic and Trinajstic) is known regarding their correlation, that D'(T)=4W(T)-n(n-1)for a tree T with n vertices. In …