Research article

Maximum $ H $-index of bipartite network with some given parameters

  • Received: 23 January 2021 Accepted: 04 March 2021 Published: 10 March 2021
  • MSC : 05C09, 05C92

  • 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, 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.

    Citation: Shahid Zaman, Fouad A. Abolaban, Ali Ahmad, Muhammad Ahsan Asim. Maximum $ H $-index of bipartite network with some given parameters[J]. AIMS Mathematics, 2021, 6(5): 5165-5175. doi: 10.3934/math.2021306

    Related Papers:

  • 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, 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.



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