论文标题

新的传输不规则化学图

New transmission irregular chemical graphs

论文作者

Xu, Kexiang, Tian, Jing, Klavžar, Sandi

论文摘要

(化学)图$ g $的顶点$ v $的传输是从$ v $到$ g $的其他顶点的距离之和。如果任何两个$ g $的顶点具有不同的传输,则$ g $是变速箱不规则图。结果表明,对于任何奇数$ n \ geq 7 $,都存在变速器不规则的化学树$ n $。提供了一种结构,可产生新的变速箱不规则(化学)树。另外两个化学图的家族的特征是传播不规则性的特性和两个足够的条件,可以保证在添加新的边缘时保留传输不规则性。

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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