Isoperimetric Constants of (d,f)-Regular Planar Graphs

Isoperimetric Constants of (d,f )-Regular Planar Graphs

Expansion And Isoperimetric Constants For Product Graphs

Vertex and edge isoperimetric constants of graphs are studied. Using a functional-analytic approach, the growth properties, under products, of these constants is analyzed.

Growth and Isoperimetric Profile of Planar Graphs

Let Γ be a planar graph such that the volume function of Γ satisfies V (2n) ≤ CV (n) for some constant C > 0. Then for every vertex v of Γ and n ∈ N, there is a domain Ω such that B(v, n) ⊂ Ω, ∂Ω ⊂ B(v, 6n) and |∂Ω| n.

Regular Honest Graphs, Isoperimetric Numbers, and Bisection of Weighted Graphs

The edge-integrity of a graph G is I 0(G) := minfjSj + m(G S) : S Eg; where m(H) denotes the maximum order of a component of H: A graph G is called honest if its edge-integrity is the maximum possible, that is, equals the order of the graph. The only honest 2-regular graphs are the 3-, 4-, and 5-cycles. Lipman [13] proved that there are exactly twenty honest cubic graphs. In this paper we explo...

Bounds on connective constants of regular graphs

Bounds are proved for the connective constant μ of an infinite, connected, ∆-regular graph G. The main result is that μ ≥ √ ∆− 1 if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.