Original Research Article

Article volume = 2025 and issue = 1

Pages: 19–34

Article publication Date: June 18, 2026

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Edge degree Zagreb indices of graphs and its Applications

Harishchandra S. Ramane (a,∗), Aafiyaparveen Madaki (a), Vijayraj S. Kamble (a)

(a) Karnatak University, Dharwad, India.

Abstract:

Edge degree of a vertex u is defined as sum of degrees of edges which are incident to a vertex u in a graph G. In this article, we define the edge degree of first and second Zagreb indices of a graph G analogous to Zagreb index in terms of edge degree. Later, we obtain the edge degree of a vertex for some standard graphs such as path, regular graph, wheel graph, star graph, complete bipartite graph, ladder graph and friendship graph. Further linear regression analysis of the edge degree Zagreb indices with the boiling points of benzenoid hydrocarbons is carried out and analysed that the first edge degree Zagreb index has good correlation with the boiling point of benzenoid hydrocarbons.

Keywords:

Edge degree of a vertex, first edge degree Zagreb index, second edge degree Zagreb index.

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Cite this article as:
  • Harishchandra S. Ramane , Aafiyaparveen Madaki , Vijayraj S. Kamble, Edge degree Zagreb indices of graphs and its Applications, Communications in Combinatorics, Cryptography & Computer Science, 2025(1), PP.19–34, 2026
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