Liu, Hechao; You, Lihua; Tang, Zikai On the revised edge-Szeged index of graphs. (English) Zbl 1464.92311 Iran. J. Math. Chem. 10, No. 4, 279-293 (2019). Summary: The revised edge-Szeged index of a connected graph \(G\) is defined as \(\mathrm{Sz}_e^*(G)=\sum_{e=uv \in E(G)}\left(m_u(e|G)+\frac{(m_0(e|G)}{2}\right)\left(m_v(e|G)+\frac{(m_0(e|G)}{2}\right)\), where \(m_u(e|G)\), \(m_v(e|G)\) and \(m_0(e|G)\) are, respectively, the number of edges of \(G\) lying closer to vertex \(u\) than to vertex \(v\), the number of edges of \(G\) lying closer to vertex \(v\) than to vertex \(u\), and the number of edges equidistant to \(u\) and \(v\). In this paper, we give an effective method for computing the revised edge-Szeged index of unicyclic graphs and using this result we identify the minimum revised edge-Szeged index of conjugated unicyclic graphs (i.e., unicyclic graphs with a perfect matching). We also give a method of calculating revised edge-Szeged index of the joint graph. Cited in 3 Documents MSC: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 05C92 Chemical graph theory Keywords:revised edge-Szeged index; conjugated unicyclic graph; join graph PDFBibTeX XMLCite \textit{H. Liu} et al., Iran. J. Math. Chem. 10, No. 4, 279--293 (2019; Zbl 1464.92311) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.