Vertex vulnerability parameters of Kronecker products of complete graphs
Information Processing Letters
Super connectivity of Kronecker products of graphs
Information Processing Letters
Note: Wiener and vertex PI indices of Kronecker products of graphs
Discrete Applied Mathematics
The Ultimate Categorical Independence Ratio of Complete Multipartite Graphs
SIAM Journal on Discrete Mathematics
On edge connectivity of direct products of graphs
Information Processing Letters
On some topological indices of the tensor products of graphs
Discrete Applied Mathematics
On the super connectivity of Kronecker products of graphs
Information Processing Letters
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The tensor product of two graphs, G and H, has a vertex set V(G) × V(H) and an edge between (u,v) and (u′,v′) iff both u u′ ∈ E(G) and v v′ ∈ E(H). Let A(G) denote the limit of the independence ratios of tensor powers of G, lim, α(Gn)-|V(Gn)|. This parameter was introduced in [Brown, Nowakowski, Rall, SIAM J Discrete Math 9 (1996), 290–300], where it was shown that A(G) is lower bounded by the vertex expansion ratio of independent sets of G. In this article we study the relation between these parameters further, and ask whether they are in fact equal. We present several families of graphs where equality holds, and discuss the effect the above question has on various open problems related to tensor graph products. © 2006 Wiley Periodicals, Inc. J Graph Theory