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Vertex PI indices of four sums of graphs. (English) Zbl 1228.05248
Summary: Suppose that \(e\) is an edge of a graph \(G\). Denote by \(m_{e}(G)\) the number of vertices of \(G\) that are not equidistant from both ends of \(e\). Then the vertex PI index of \(G\) is defined as the summation of \(m_{e}(G)\) over all edges \(e\) of \(G\). In this paper we give the explicit expressions for the vertex PI indices of four sums of two graphs in terms of other indices of two individual graphs, which correct the main results in a paper published in [S. Li, H. Bian, G. Wang, and H. Yu, “Vertex PI indices of some sums of graphs,” Ars Comb. 98, 63–71 (2011)].

05C76 Graph operations (line graphs, products, etc.)
Full Text: DOI
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