三点传递图张量乘积中的独立集

IF 0.6 4区数学 Q3 MATHEMATICS

Taiwanese Journal of Mathematics Pub Date : 2021-03-25 DOI:10.11650/TJM/210104

Hu Mao, Huajun Zhang

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引用次数: 0

摘要

图G1、G2和G3的张量积T（G1、G2、G3）定义为V T（G1，G2，G3）=V（G1）×V（G2）×V。从这个定义中，很容易看出，在投影下两个因子的两个独立集合的直接乘积的前像是T（G1，G2，G3）的独立集合。因此，αT（G1，G2，G3）≥max{α（G1）α（G2）|G3|，α（G1。本文证明了当G1和G2是顶点传递图，而G3是圆图、Kneer图或置换图时，等式成立。此外，在这种情况下，确定T（G1，G2，G3）的所有最大独立集的结构。

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Independent Sets in Tensor Products of Three Vertex-transitive Graphs

The tensor product T (G1, G2, G3) of graphs G1, G2 and G3 is defined by V T (G1, G2, G3) = V (G1)× V (G2)× V (G3) and ET (G1, G2, G3) = {[(u1, u2, u3), (v1, v2, v3)] : |{i : (ui, vi) ∈ E(Gi)}| ≥ 2}. From this definition, it is easy to see that the preimage of the direct product of two independent sets of two factors under projections is an independent set of T (G1, G2, G3). So αT (G1, G2, G3) ≥ max{α(G1)α(G2)|G3|, α(G1)α(G3)|G2|, α(G2)α(G3)|G1|}. In this paper, we prove that the equality holds if G1 and G2 are vertex-transitive graphs and G3 is a circular graph, a Kneser graph, or a permutation graph. Furthermore, in this case, the structure of all maximum independent sets of T (G1, G2, G3) is determined.

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来源期刊

Taiwanese Journal of Mathematics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.