Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

" Provides the first comprehensive treatment of theoretical, algorithmic, and application
aspects of domination in graphs-discussing fundamental results and major research …

We consider powers of regular graphs defined by the weak graph product and give a
characterization of maximum-size independent sets for a wide family of base graphs which …

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 uu′∈ E (G) and vv′∈ E (H). Let A (G) denote the limit …

Let G be a connected bipartite graph. An involution α of G that preserves the bipartition of G
is called bipartite. Let G^α be the graph obtained from G by adding to G the natural perfect …

Asymptotic values of the Hall-ratio for graph powers - ScienceDirect Skip to main contentSkip
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Abstract In Nowakowski and Rall listed a series of conjectures involving several different
graph products. In particular, they conjectured that i (G× H)≥ i (G) i (H) where i (G) is the …

Weighted generalizations of Hoffman's ratio bound on the independence number of a
regular graph are surveyed. Several known bounds are reviewed as special cases of …

Abstract Brown, Nowakowski and Rall defined the ultimate categorical independence ratio
of a graph G as A (G)= lim k→∞ i (G× k), where i (G)= α (G)| V (G)| denotes the …

The main focus of this work is the study of various parameters of high powers of a given
graph, under different definitions of the product operator. The problems we study and the …