论文标题
关于偏心连通性指数和图形偏心距离之和之间的差异
On the difference between the eccentric connectivity index and eccentric distance sum of graphs
论文作者
论文摘要
图$ g $的偏心连接索引为$ξ^c（g）= \ sum_ {v \ in v（g）} \ varepsilon（v）°（v）$（v）$，而偏心距离为$ξ^d（g）= \ sum__ = \ sum_ { $ \ varepsilon（v）$是$ v $的偏心，$ d（v）$ $ v $和其他顶点之间的距离之和。 $ξ^d（g） - ξ^c（g）$上的下部和上限为任意图$ g $。直径最多$ 2 $的常规图形和与完整图的鸡尾酒会图相结合的图表，分别达到了两个平等。 $ξ^d（t） - ξ^c（t）$上的尖锐下限和上限为任意树。还给出了$ξ^d（g）+ξ^c（g）$的尖锐下限，并给出了$ g $的$ g $，并且证明了带有给定半径的图形$ g $在$ξ^d（g）上的尖锐下限。
The eccentric connectivity index of a graph $G$ is $ξ^c(G) = \sum_{v \in V(G)}\varepsilon(v)°(v)$, and the eccentric distance sum is $ξ^d(G) = \sum_{v \in V(G)}\varepsilon(v)D(v)$, where $\varepsilon(v)$ is the eccentricity of $v$, and $D(v)$ the sum of distances between $v$ and the other vertices. A lower and an upper bound on $ξ^d(G) - ξ^c(G)$ is given for an arbitrary graph $G$. Regular graphs with diameter at most $2$ and joins of cocktail-party graphs with complete graphs form the graphs that attain the two equalities, respectively. Sharp lower and upper bounds on $ξ^d(T) - ξ^c(T)$ are given for arbitrary trees. Sharp lower and upper bounds on $ξ^d(G)+ξ^c(G)$ for arbitrary graphs $G$ are also given, and a sharp lower bound on $ξ^d(G)$ for graphs $G$ with a given radius is proved.
