Original Research Article

Article volume = 2025 and issue = 1

Pages: 40–49

Article publication Date: July 05, 2026

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Edge degree Zagreb indices of certain class of trees and their application

Harishchandra S. Ramane(*), Vijayraj S. Kamble, and Aafiyaparveen Madaki

Department of Mathematics, Karnatak University, Pavate Nagar, Dharwad, Karnataka 580003, India.

Abstract:

The edge degree of a vertex of a graph $G$ is defined as sum of degrees of all the edges incident to it. In this article, with respect to edge degree of a vertex, we introduce first and second Edge degree Zagreb indices of graph $G$ and are defined as $EDZ_1=\sum_{uv\in E(G)}\left[ {ed_{(u)}+ed_{(v)}}\right] $ and $EDZ_2=\sum_{uv \in E(G)}\left[ {ed_{(u)}\ ed_{(v)}}\right]$ respectively. Later, we compute first and second edge degree Zagreb indices of well known trees such as Kragujevac trees, bistar trees and tristar trees. Further carried out linear regression analysis of first and second edge degree Zagreb indices of underlying molecular graphs of octane isomers which are trees.

Keywords:

Edge degree of a vertex, Edge degree Zagreb indices, Kragujevac tree, Bistar tree, Tristar tree.

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Cite this article as:
  • Harishchandra S. Ramane, Vijayraj S. Kamble, and Aafiyaparveen Madaki, Edge degree Zagreb indices of certain class of trees and their application, Communications in Combinatorics, Cryptography & Computer Science, 2025(1), PP.40–49, 2026
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