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On interval transmission irregular graphs
Journal of Applied Mathematics and Computing ( IF 2.4 ) Pub Date : 2021-03-01 , DOI: 10.1007/s12190-021-01513-0
Salem Al-Yakoob , Dragan Stevanović

Transmission of a vertex v of a connected graph G is the sum of distances from v to all other vertices in G. Graph G is transmission irregular (TI) if no two of its vertices have the same transmission, and G is interval transmission irregular (ITI) if it is TI and the vertex transmissions of G form a sequence of consecutive integers. Here we give a positive answer to the question of Dobrynin [Appl Math Comput 340 (2019), 1–4] of whether infinite families of ITI graphs exist.



中文翻译:

关于间隔传输不规则图

连通图G的顶点v的 传输 是从vG中所有其他顶点 的距离之和 。图ģ是传输不规则(TI),如果没有它的两个顶点具有相同的传输,并且ģ是间隔传输不规则(ITI),如果它是TI和的顶点传输ģ形成连续整数的序列。在这里,我们对Dobrynin [Appl Math Comput 340(2019),1-4]是否存在无限个ITI图族的问题给出了肯定的答案。

更新日期:2021-03-02
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