On the diameter and connectivity of bipartite Kneser type-k graphs

Articles in Press

Document Type : Original Manuscript

Authors

1 Department of Mathematics, University college, University of Kerala, India

2 Department of mathematics, University of Kerala

3 Professor, Department of Mathematics, University College, University of Kerala, Thiruvananthapuram, Kerala

Abstract

Let n∈Z+, n>1, and k be an integer, 1≤k≤n−1. The graph HT(n,k) is defined as a graph with vertex set V, as all non-empty subsets of Sn={1,2,3,…,n}. It is a bipartite graph with partition (V1,V2), in which V1 contains the k-element subsets of Sn and V2 contains i-element subsets of Sn, for 1≤i≤n, i≠k. An edge exists between a vertex U∈V1 and a vertex W∈V2 if either U⊂W or W⊂U. In this paper, we established formulae for the number of edges, vertex connectivity, edge connectivity and degree polynomial. Then, we analysed the clique number and diameter of HT(n,k). We also verified that the graphs HT(n,k) and HT(n,n−k) are isomorphic. Degree-based topological indices such as the general Randic connectivity index, the first general Zagreb index and the general sum connectivity index are also computed. Also, we proved that the line graph of HT(n,k) is not a bipartite graph.

Keywords

Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 09 April 2024

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