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Several distance based indices for complement of graphs. (English) Zbl 1463.05105

Summary: A graph \(G\) is said to have property \(P\) if for every pair of its adjacent vertices \(x\) and \(y\) there exists a vertex \(z\) such that \(z\) is not adjacent to \(x\) and \(y\). In this paper, we establish an explicit formula to calculate the several graph indices for the complement of any graph \(G\) having above property. As a corollary we obtain the several graph indices for the complement of certain derived graphs.

MSC:

05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)
05C12 Distance in graphs
05C76 Graph operations (line graphs, products, etc.)
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References:

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