The first Leap Zagreb coindex of some graph operations

Document Type : Original paper

Authors

Department of Mathematics, Yuvraja's College, University of Mysore, Mysuru-570005, India

Abstract

In the last years, Naji et al. have introduced leap Zagreb indices conceived depending on the second degrees of vertices, where the second degree of a vertex $v$ in a graph $G$ is equal to the number of its second neighbors and denoted by $d_2(v/G)$.  Analogously, the leap Zagreb coindices were introduced by Ferdose and Shivashankara. The first leap Zagreb coindex of a graph is defined as  $\overline{L_1}(G)=\sum_{uv\not\in E_2(G)}(d_2(u)+d_2(v))$, where $E_2(G)$ is the 2-distance (second) edge set of $G$, In this paper, we present explicit exact expressions for the first leap Zagreb coindex $\overline{L_1}(G)$ of some graph operations.

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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 2
June 2025
Pages 483-495

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