2013/05/13 by S. C. López, López, S. C., F. A. Muntaner-Batle +1
Mathematics · #05C40 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C40
paper · pdf · doi:10.48550/arxiv.1305.2729
14 pages
arxiv created 2013/05/13 · arxiv updated 2013/05/14
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∈ Γ. Consider any function h:E(D)\longrightarrowΓ. Then the product D⊗h Γ is the digraph with vertex set V(D)× V and ((a,x),(b,y))∈ E(D⊗hΓ) if and only if (a,b)∈ E(D) and (x,y)∈ E(h (a,b)). In this paper, we introduce the undirected version of the ⊗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 ⊗h-product of graphs.