关于传输不规则图和长垂径

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2024-07-31 DOI:10.1016/j.amc.2024.128918

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引用次数: 0

摘要

连通图中一个顶点的传输是该顶点到所有其他顶点的距离之和。如果一个图中没有两个顶点具有相同的传输，那么这个图就是传输不规则图（TI）。Xu 等人（2023 年）最近要求建立从现有图中构造新 TI 图的方法，以及在每个偶数阶上存在化学 TI 图的问题。我们证明了在某些条件下，可以从现有的 TI 图中得到新的 TI 图，方法是在 TI 图的每个顶点上附加等长的下垂路径，或者在 TI 图的一个顶点上附加两条连续长度的下垂路径。我们还证明了几乎所有偶数阶都存在化学 TI 图。

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On transmission-irregular graphs and long pendent paths

The transmission of a vertex in a connected graph is the sum of distances from that vertex to all other vertices. A graph is transmission-irregular (TI) if no two of its vertices have the same transmission. Xu et al. (2023) [3] recently asked to establish methods for constructing new TI graphs from the existing ones and also about the existence of chemical TI graphs on every even order. We show that, under certain conditions, new TI graphs can be obtained from the existing TI graph G either by attaching pendent paths of equal length to every vertex of G or by attaching two pendent paths of consecutive lengths to one vertex of G. We also show the existence of chemical TI graphs for almost all even orders.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.