Tricyclic graphs with maximal revised Szeged index

Abstract

The revised Szeged index of a graph $G$ is defined as $S{z}^{\ast }(G)={\sum }_{e=uv\in E}(n_u(e)+n_0(e)/2)(n_v(e)+n_0(e)/2),$ where $n_u(e)$ and $n_v(e)$ are, respectively, the number of vertices of $G$ lying closer to vertex $u$ than to vertex $v$ and the number of vertices of $G$ lying closer to vertex $v$ than to vertex $u$, and $n_0(e)$ is the number of vertices equidistant to $u$ and $v$. In this paper, we give an upper bound of the revised Szeged index for a connected tricyclic graph, and also characterize those graphs that achieve the upper bound.

14 pages. arXiv admin note: text overlap with arXiv:1104.2122

References in corpus (2)

• Note on PI and Szeged indices
• On a relation between the Szeged index and the Wiener index for bipartite graphs

Cited by in corpus (2)

• On a relation between the Szeged index and the Wiener index for bipartite graphs
• The (revised) Szeged index and the Wiener index of a nonbipartite graph