A METHOD FOR COMPUTING THE EDGE-HYPER-WIENER INDEX OF PARTIAL CUBES AND AN ALGORITHM FOR BENZENOID SYSTEMS

Applicable Analysis and Discrete Mathematics

article

Niko Tratnik¹ 

[1] Faculty of Natural Sciences and Mathematics University of Maribor Slovenia

关键词: Edge-hyper-Wiener index;    edge-Wiener index;    partial cube;    benzenoid system;    linear polyacene.;   

DOI  :  10.2298/AADM1801126T

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

The edge-hyper-Wiener index of a connected graph G is defined asWWe(G) = 12P{e,f}⊆E(G)d(e, f) + 12P{e,f}⊆E(G)d(e, f)2. We develop amethod for computing the edge-hyper-Wiener index of partial cubes, whichconstitute a large class of graphs with a lot of applications. It is also shownhow the method can be applied to trees. Furthermore, an algorithm forcomputing the edge-hyper-Wiener index of benzenoid systems is obtained.Moreover, the algorithm is used to recalculate already known closed formulasfor the edge-Wiener index and the edge-hyper-Wiener index of linear polyacenes. Finally, the method is presented on a benzenoid system with morecomplicated structure.

【 授权许可】

Unknown