Results 31 to 40 of about 4,536 (107)
Quantum automorphism groups of lexicographic products of graphs
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract Sabidussi's theorem [Duke Math. J. 28 (1961), 573–578] gives necessary and sufficient conditions under which the automorphism group of a lexicographic product of two graphs is a wreath product of the respective automorphism groups. We prove a quantum version of Sabidussi's theorem for finite graphs, with the automorphism groups replaced by ...
Arnbjörg Soffía Árnadóttir +4 more
wiley +1 more source
Cladistics, Volume 41, Issue 1, Page 1-27, February 2025.Abstract Here, we propose, prove mathematically and discuss maximum and minimum measures of maximum parsimony evolution across 12 discrete phylogenetic character types, classified across 4467 morphological and molecular datasets. Covered character types are: constant, binary symmetric, multistate unordered (non‐additive) symmetric, multistate linear ...
Jennifer F. Hoyal Cuthill +1 more
wiley +1 more source
Strong arc decompositions of split digraphs
Journal of Graph Theory, Volume 108, Issue 1, Page 5-26, January 2025.Abstract A strong arc decomposition of a digraph D = ( V , A ) is a partition of its arc set A into two sets A 1 , A 2 such that the digraph D i = ( V , A i ) is strong for i = 1 , 2. Bang‐Jensen and Yeo conjectured that there is some K such that every K‐arc‐strong digraph has a strong arc decomposition. They also proved that with one exception on four
Jørgen Bang‐Jensen, Yun Wang
wiley +1 more source
Immersions of Directed Graphs in Tournaments
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT Recently, Draganić, Munhá Correia, Sudakov and Yuster (2022) showed that every tournament on (2+o(1))k2$$ \left(2+o(1)\right){k}^2 $$ vertices contains a 1‐subdivision of a transitive tournament on k$$ k $$ vertices, which is tight up to a constant factor. We prove a counterpart of their result for immersions.
António Girão, Robert Hancock
wiley +1 more source
Journal of Mathematics, Volume 2025, Issue 1, 2025.The construction of circuits formed by reduced quadratic irrational numbers (RQINs) under the action of Mobius groups has attracted growing attention due to their deep algebraic structure and wide range of applications. Such orbits and circuits play a significant role in modern cryptographic systems, particularly in the design of robust substitution ...
Muhammad Haris Mateen +5 more
wiley +1 more source
Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.Abstract Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$, the m$m$‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$. The classical Shi arrangement (m=0$m=0$) was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for W$W$.
Matthew Dyer +3 more
wiley +1 more source
The Homomorphism Poset of K_{2,n}
, 2012 A geometric graph is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. Two geometric realizations of a simple graph are geo-isomorphic if there is a vertex bijection between them that ...
Cockburn, Sally, Song, Yonghyun
core
The structure of digraphs with excess one
Journal of Graph Theory, Volume 106, Issue 3, Page 411-434, July 2024.Abstract A digraph G $G$ is k $k$‐geodetic if for any (not necessarily distinct) vertices u,v $u,v$ there is at most one directed walk from u $u$ to v $v$ with length not exceeding k $k$. The order of a k $k$‐geodetic digraph with minimum out‐degree d $d$ is bounded below by the directed Moore bound M(d,k)=1+d+d2+⋯+dk $M(d,k)=1+d+{d}^{2}+\cdots +{d}^{k}
James Tuite
wiley +1 more source
Minimum Cost Homomorphisms to Locally Semicomplete and Quasi-Transitive Digraphs
, 2007 For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$ such that $uv\in A(G)$ implies $f(u)f(v)\in A(H)$. If, moreover, each vertex $u \in V(G)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of a ...
Gupta, A. +4 more
core +2 more sources
New eigenvalue bound for the fractional chromatic number
Journal of Graph Theory, Volume 106, Issue 1, Page 167-181, May 2024.Abstract Given a graph G $G$, we let s+(G) ${s}^{+}(G)$ denote the sum of the squares of the positive eigenvalues of the adjacency matrix of G $G$, and we similarly define s−(G) ${s}^{-}(G)$. We prove that χf(G)≥1+maxs+(G)s−(G),s−(G)s+(G) ${\chi }_{f}(G)\ge 1+\max \left\{\frac{{s}^{+}(G)}{{s}^{-}(G)},\frac{{s}^{-}(G)}{{s}^{+}(G)}\right\}$ and thus ...
Krystal Guo, Sam Spiro
wiley +1 more source