论文标题
逐步传播不规则图的极端结果
Extremal results on stepwise transmission irregular graphs
论文作者
论文摘要
连接图$ g $的顶点$ v $的传输$ {\ rm tr} _g（v）$是$ v $与$ g $中所有其他顶点之间的距离之和。 $ g $是逐步传输不规则（STI）图，如果$ | {\ rm tr} _g（u） - {\ rm tr} _g（v）| = 1 $保留E（g）$中的每个边缘$ UV \。在本文中，关于STI图的极端结果，就大小和不同的度量特性得到了证明。在所有情况下，两个极端家庭都出现了，平衡的奇数秩和奇数周期的完整二分图。
The transmission ${\rm Tr}_G(v)$ of a vertex $v$ of a connected graph $G$ is the sum of distances between $v$ and all other vertices in $G$. $G$ is a stepwise transmission irregular (STI) graph if $|{\rm Tr}_G(u) - {\rm Tr}_G(v)| =1$ holds for each edge $uv \in E(G)$. In this paper, extremal results on STI graphs with respect to the size and different metric properties are proved. Two extremal families appear in all the cases, balanced complete bipartite graphs of odd order and the so called odd hatted cycles.
