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The prime graph $Γ (G)$ of a finite group $G$ is defined as follows: the set of vertices is $π (G)$ , the set of primes dividing the order of $G$ , and two vertices $p$ , $q$ are joined by an edge (we write $p \sim q$ ) if and only if there exists an element in $G$ of order $p q$ . We study the groups $G$ such that the prime graph $Γ (G)$ is a tree, proving that, in this case, $|π (G)| \leq 8$ .

Groups with the same prime graph as an almost sporadic simple group.

Khosravi, Behrooz (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Growth functions and automatic groups.

Epstein, David B.A., Iano-Fletcher, Anthony R., Zwick, Uri (1996)

Experimental Mathematics

Growth in ${SL}_{3} (ℤ / p ℤ)$

H. A. Helfgott (2011)

Journal of the European Mathematical Society

Growth of graph powers.

Pokrovskiy, A. (2011)

The Electronic Journal of Combinatorics [electronic only]

Grundy number of graphs

Brice Effantin, Hamamache Kheddouci (2007)

Discussiones Mathematicae Graph Theory

The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i-1) vertices colored with each color j, 1 ≤ j ≤ i -1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally, we present an...

Guessing secrets.

Chung, Fan, Graham, Ronald, Leighton, Tom (2001)

The Electronic Journal of Combinatorics [electronic only]

$H$ -convex graphs

Gary Chartrand, Ping Zhang (2001)

Mathematica Bohemica

For two vertices $u$ and $v$ in a connected graph $G$ , the set $I (u, v)$ consists of all those vertices lying on a $u - v$ geodesic in $G$ . For a set $S$ of vertices of $G$ , the union of all sets $I (u, v)$ for $u, v \in S$ is denoted by $I (S)$ . A set $S$ is convex if $I (S) = S$ . The convexity number $c o n (G)$ is the maximum cardinality of a proper convex set in $G$ . A convex set $S$ is maximum if $| S | = c o n (G)$ . The cardinality of a maximum convex set in a graph $G$ is the convexity number of $G$ . For a nontrivial connected graph $H$ , a connected graph $G$ is an $H$ -convex graph if $G$ contains...

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Ground state incongruence in 2D spin glasses revisited.

Group inverses of matrices with path graphs.

Groupoids with non-associative triples on the diagonal

Groups acting on products of trees, tiling systems and analytic $K$ -theory.

Groups and homogeneous graphs

Groups and polar graphs

Groups generated by k-root subgroups.

Groups in which the prime graph is a tree

Groups with the same prime graph as an almost sporadic simple group.

Growth functions and automatic groups.

Growth in ${SL}_{3} (ℤ / p ℤ)$

Growth of graph powers.

Grundy number of graphs

Guessing secrets.

$H$ -convex graphs

$H$ -decompositions of $r$ -graphs when $H$ is an $r$ -graph with exactly 2 edges.

$H$ -free graphs of large minimum degree.

$h^{*}$ -vectors, Eulerian polynomials and stable polytopes of graphs.

Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property.

Hadwiger numbers of finite graphs

Currently displaying 2041 – 2060 of 5365