The Wiener Index of r-Uniform Hypergraphs

The Wiener index of a hypergraph is the sum of distances between all pairs of vertices of the hypergraph. In this paper, we first investigate the Wiener index of some special r-uniform paths and r-uniform cycles. The Wiener index of different kinds of 3-uniform paths were also considered. Then we explore the lower bound of Wiener index in a r-uniform hypergraph on n vertices with a given circumference which is the maximum length of a cycle in a hypergraph. In the last part, we propose the concept of the chemical bond-Wiener index of a graph, which is the sum of the distances between all pairs of chemical bonds of a graph, considering the removing of hydrogen atoms. The polyphenyl chains with minimum and maximum chemical bond-Wiener indices among all the polyphenyl chains with h hexagons were completely determined.

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