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Extremal tetracyclic graphs with respect to the first and second Zagreb indices. (English) Zbl 1463.05087

Summary: The first Zagreb index, \(M_1(G)\), and second Zagreb index, \(M_2(G)\), of the graph \(G\) is defined as \(M_1(G)=\sum_{v\in V(G)}d^2(v)\) and \(M_2(G)= \sum_{e=uv\in E(G)} d(u)d(v)\), where \(d(u)\) denotes the degree of vertex \(u\). In this paper, the first and second maximum values of the first and second Zagreb indices in the class of all \(n\)-vertex tetracyclic graphs are presented.

MSC:

05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)
05C07 Vertex degrees
05C35 Extremal problems in graph theory
05C75 Structural characterization of families of graphs
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