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arXiv · 1305.2729

Connectivity and other invariants of generalized products of graphs

S. C. López·F. A. Muntaner-Batle
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Abstract

Figueroa-Centeno et al. introduced the following product of digraphs: let $D$ be a digraph and let $Γ$ be a family of digraphs such that $V(F)=V$ for every $F\in Γ$. Consider any function $h:E(D)\longrightarrowΓ$. Then the product $D\otimes_{h} Γ$ is the digraph with vertex set $V(D)\times V$ and $((a,x),(b,y))\in E(D\otimes_hΓ)$ if and only if $(a,b)\in E(D)$ and $(x,y)\in E(h (a,b))$. In this paper, we introduce the undirected version of the $\otimes_h$-product, which is a generalization of the classical direct product of graphs and, motivated by it, we also recover a generalization of the classical lexicographic product of graphs that was introduced by Sabidussi en 1961. We study connectivity properties and other invariants in terms of the factors. We also present a new intersection graph that emerges when we characterize the connectivity of $\otimes_h$-product of graphs.

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S. C. López, F. A. Muntaner-Batle. 2013-05-13. Connectivity and other invariants of generalized products of graphs. https://arxiv.org/abs/1305.2729

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