Dragan Stevanović, Mohammad Ghebleh, Gilles Caporossi, Ambat Vijayakumar, Sanja Stevanović
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引用次数: 0
摘要
简单图 G 的顶点 v 的三角形度是 G 中包含 v 的三角形的数目。如果一个简单图的所有顶点都有不同的三角形度，那么这个图就是三角形模糊图。Berikkyzy 等人[Discrete Math. 347 (2024) 113695]最近提出了一个问题：是否存在三角形不明显的正则图？在这里，我们首先展示了正则、三角形不明显图的例子，然后证明对于每个自然数 k，都存在一个 \(2^k\) 正则三角形不明显图的族，它们都具有相同的阶数和大小。
The triangle-degree of a vertex v of a simple graph G is the number of triangles in G that contain v. A simple graph is triangle-distinct if all its vertices have distinct triangle-degrees. Berikkyzy et al. [Discrete Math. 347 (2024) 113695] recently asked whether there exists a regular graph that is triangle-distinct. Here we first showcase the examples of regular, triangle-distinct graphs, and then show that for every natural number k there exists a family of \(2^k\) regular triangle-distinct graphs, all having the same order and size.
期刊介绍：
Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics).
The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.
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