Maximum \(H\)-index of bipartite network with some given parameters. (English) Zbl 1484.05054
Summary: 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.
MSC:
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
| 05C92 | Chemical graph theory |
Keywords:
\(H\)-index; bipartite network; matching number; independence number; cover of a network; diameterReferences:
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