The reciprocal complementary Wiener number of graphs

  • Ramin Nasiri Department of Mathematics, Imam Hossein Comprehensive University, Tehran, Iran
Keywords: Reciprocal complementary Wiener number, Distance, The Bar-Polyhex graph, The Mycielskian graph.

Abstract

The reciprocal complementary Wiener number (RCW) of a connected graph G is defined as the sum of
weights frac{1}{D+1-d_G(x,y)} over all unordered vertex pairs in a graph G, where D is the diameter of G
and d_G(x,y) is the distance between vertices x and y. In this paper, we find new bounds for RCW of
graphs, and study this invariant of two important types of graphs, named the Bar-Polyhex and the
Mycielskian graphs.

Published
2019-12-30
How to Cite
Nasiri, R. (2019). The reciprocal complementary Wiener number of graphs. Tamkang Journal of Mathematics, 50(4), 371-381. https://doi.org/10.5556/j.tkjm.50.2019.2714
Section
Papers