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arXiv · 2207.04101

On the Maximum Sigma Index of k-Cyclic Graphs

Akbar Ali·Abeer M. Albalahi·Abdulaziz M. Alanazi·Akhlaq A. Bhatti·Amjad E. Hamza
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Abstract

Let $G$ be a graph with edge set $E(G)$. Denote by $d_w$ the degree of a vertex $w$ of $G$. The sigma index of $G$ is defined as $\sum_{uv\in E(G)}(d_u-d_v)^2$. A connected graph of order $n$ and size $n+k-1$ is known as a connected $k$-cyclic graph. Abdo, Dimitrov, and Gutman [Discrete Appl. Math. 250 (2018) 57-64] characterized the graphs having the greatest sigma index over the family of all connected graphs of a fixed order. The primary goal of the present note is to determine graphs possessing the greatest sigma index from the class of all connected $k$-cyclic graphs of a fixed order.

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Akbar Ali, Abeer M. Albalahi, Abdulaziz M. Alanazi, Akhlaq A. Bhatti, Amjad E. Hamza. 2022-07-08. On the Maximum Sigma Index of k-Cyclic Graphs. https://arxiv.org/abs/2207.04101

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