Abstract
The Wiener index W(G) and the edge-Wiener index We(G) of a graph G are defined as the sum of all distances between pairs of vertices in a graph G and the sum of all distances between pairs of edges in G, respectively. The Wiener index, due to its correlation with a large number of physico-chemical properties of organic molecules and its interesting and non-trivial mathematical properties, has been extensively studied in both theoretical and chemical literature. The edge-Wiener index of G is nothing but the Wiener index of the line graph of G. The concept of line graph has been found various applications in chemical research. In this paper, we show that if G is a catacondensed hexagonal system with h hexagons and has t linear segments S1,S2,…,St of lengths l(Si)=li(1≤i≤t), then We(G)=2516W(G)+116(120h2+94h+29)−14∑i=1t(li−1)2. Our main result reduces the problems on the edge-Wiener index to those on the Wiener index in the catacondensed hexagonal systems, which makes the former ones easier.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
