A 2-Bisection with Small Number of Monochromatic Edges of a Claw-Free Cubic Graph

The Maximum Number of Edges in a Strongly Multiplicative Graph

Upper minus domination in a claw-free cubic graph

We show in this paper that the upper minus domination number −(G) of a claw-free cubic graph G is at most 1 2 |V (G)|. © 2006 Published by Elsevier B.V.

the maximum number of edges in a strongly multiplicative graph

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The asymptotic number of claw-free cubic graphs

Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for Hn. Here

Uniform Number of a Graph

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...