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arXiv · 2211.04836

New transmission irregular chemical graphs

Kexiang Xu·Jing Tian·Sandi Klavžar
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Abstract

The transmission of a vertex $v$ of a (chemical) graph $G$ is the sum of distances from $v$ to other vertices in $G$. If any two vertices of $G$ have different transmissions, then $G$ is a transmission irregular graph. It is shown that for any odd number $n\geq 7$ there exists a transmission irregular chemical tree of order $n$. A construction is provided which generates new transmission irregular (chemical) trees. Two additional families of chemical graphs are characterized by property of transmission irregularity and two sufficient condition provided which guarantee that the transmission irregularity is preserved upon adding a new edge.

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Kexiang Xu, Jing Tian, Sandi Klavžar. 2022-11-09. New transmission irregular chemical graphs. https://arxiv.org/abs/2211.04836

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