A study on the minimum degree wiener index of graphs

Abstract

In this paper, we introduced a new distance-based index called the minimum degree Wiener index, which is the sum of distances between all unordered pairs of vertices with the minimum degree. Additionally, a matrix related to this index was introduced, and it was discovered that the sum of entries in each row was the same for some classes of graphs, contrary to many graph-related matrices. In particular, we determined the minimum degree Wiener index of the bipartite Kneser graph, bipartite Kneser type-k graphs, Johnson graph and the set inclusion graphs. The terminal Wiener index of a graph G is the sum of distances between all unordered pairs of pendant vertices of G. Also, we determined Wiener index, hyper Wiener index and corresponding polynomials of the bipartite Kneser type-k graphs for k = 2, 3.