Results 1 to 10 of about 18,324 (228)

A Coarse Geometric Approach to Graph Layout Problems

Journal of Graph Theory, Volume 113, Issue 2, Page 169-194, October 2026.
ABSTRACT We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are ...
Wanying Huang, David Hume, Samuel J. Kelly, Ryan Lam   +3 more
wiley   +1 more source

Abelian number fields with frobenian conditions

Mathematika, Volume 72, Issue 4, October 2026.
Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
wiley   +1 more source

Full Automorphism Group of (m, 2)-Graph in Finite Classical Polar Spaces

Axioms
Let Q be the finite classical polar space of rank ν≥1 over Fq, and Qm be the set of all m-dimensional subspaces of Q. In this paper, we introduce the (m, 2)-graph with Qm as its vertex set, and two vertices P, Q are adjacent if and only if P + Q is an (m
Yang Zhang, Shuxia Liu, Liwei Zeng
doaj   +1 more source

Signed Projective Cubes, a Homomorphism Point of View

Journal of Graph Theory, Volume 113, Issue 1, Page 38-56, September 2026.
ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen, Reza Naserasr, Alessandra Sarti   +2 more
wiley   +1 more source

On θ-commutators and the corresponding non-commuting graphs

Open Mathematics, 2017
The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other ...
Shalchi S., Erfanian A., Farrokhi DG M.
doaj   +1 more source

Acylindrical visual splittings and the Tits alternative for Artin groups

Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.
Abstract We give a necessary and sufficient condition on a visual splitting of an Artin group satisfying the conclusions of two well‐known conjectures to be acylindrical, and demonstrate how this can be used to provide a large class of novel examples of Artin groups that satisfy the Tits alternative.
William D. Cohen
wiley   +1 more source

The Orbits of Twisted Crossed Cubes

Mathematics
Two vertices u and v in a graph G=(V,E) are in the same orbit if there exists an automorphism ϕ of G such that ϕ(u)=v. The orbit number of a graph G, denoted by Orb(G), is the number of orbits that partition V(G).
Jia-Jie Liu
doaj   +1 more source

CLASSIFICATION OF FINITE p-GROUPS WITH METACYCLIC AUTOMORPHISMS GROUP

پژوهش‌های ریاضی, 2021
In this paper we classify finite p-groups (p>2 )  with metacyclic automorphism  group.  Particularly we prove that the automorphism group of group G is metacyclic if and only if  G is cyclic of order  p^n.
Shirin Fouladi
doaj  

The probability of generating finite and profinite groups

Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.
Abstract Famously, every finite simple group G$G$ can be generated by a pair of elements. Moreover, Liebeck and Shalev (1995) proved that the probability that a pair of elements generate G$G$ tends to 1 as |G|→∞$|G| \rightarrow \infty$. In this paper, we generalize this theorem of Liebeck and Shalev. Work of Lucchini and Menegazzo (1997) implies that a
Scott Harper, Martyn Quick
wiley   +1 more source

ON THE GROWTH OF GROUPS AND AUTOMORPHISMS [PDF]

International Journal of Algebra and Computation, 2005
We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.
openaire   +4 more sources