Classification of 3-GNDB graphs

Document Type : Research Paper

Authors

1 Department of Mathematics, Islamic Azad University, Nazarabad Branch, Nazarabad, Iran

2 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

3 Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran

Abstract

A nonempty graph $\Gamma$ is called generalized 3-distance-balanced, (3-$GDB$) whenever for every edge $ab$, $|W_{ab}|=3|W_{ba}|$ or conversely. As well as a graph $\Gamma$ is called generalized 3-nicely distance-balanced (3-$GNDB$) whenever for every edge $ab$ of $\Gamma$, there exists a positive integer $\gamma_\Gamma$, such that: $|W_{ba}|=\gamma_\Gamma$.In this paper, we classify 3-$GNDB$ graphs with, $\gamma_\Gamma\in \{1,2\}$.

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References

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Journal of Algebra and Related Topics
Volume 13, Issue 1
July 2025
Pages 53-60

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