Weighted topological indices of graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, College of Sciences, University of Sharjah, UAE

2 Department of Applied Mathematics, School of Engineering, Samarkand International University of Technology, Samarkand 140100, Uzbekistan

3 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I. R. Iran

Abstract

The definition of the weighted topological index associated with a degree function $\phi$ is $\Phi(G)=\sum_{uv\in E(G)}\phi(d_{u},d_{v})$, where $d_{u}$ denotes the degree of node $u$ and $\phi$ satisfies symmetric property $\phi(d_{u},d_{v})=\phi(d_{v},d_{u})$. In this paper, we characterized extremal graphs and presented several results concerning the function $\Phi(G)$ in terms of various graph invariants. Additionally, we characterize the graphs that achieve these bounds and present multiple bounds for $\Phi(G)$ for the class of cozero divisor graphs defined on commutative rings.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 25 October 2024

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