부산대학교 도서관

For any two distinct vertices u and v in a connected graph G , let l P u , v = l P be the length of u − v path P and the D–distance between u and v of G is defined as: d D u , v = min p l P + ∑ ∀ y ∈ V P deg y , where the minimum is taken over all u − v paths P and the sum is taken over all vertices of u − v path P. The D-index of G is defined as W D G = 1 / 2 ∑ ∀ v , u ∈ V G d D u , v . In this paper, we found a general formula that links the Wiener index with D-index of a regular graph G. Moreover, we obtained different formulas of many special irregular graphs. [ABSTRACT FROM AUTHOR]