Maximum H-index of bipartite network with some given parameters

作者：Zaman, Shahid; Abolaban, Fouad A.; Ahmad, Ali^*; Asim, Muhammad Ahsan

来源：AIMS Mathematics, 2021, 6(5): 5165-5175.

DOI：10.3934/math.2021306

• H-index
• bipartite network
• matching number
• independence number
• cover of a network
• diameter

A network is an abstract structure that consists of nodes that are connected by links. A bipartite network is a type of networks where the set of nodes can be divided into two disjoint sets in a way that each link connects a node from one partition with a node from the other partition. In this paper, we first determine the maximum H-index of networks in the class of all n-node connected bipartite network with matching number t. We obtain that the maximum H-index of a bipartite network with a given matching number is K-t,K-n-t. Secondly, we characterize the network with the maximum H index in the class of all the n-vertex connected bipartite network of given diameter. Based on our obtain results, we establish the unique bipartite network with maximum H-index among bipartite networks with a given independence number and cover of a network.