Results 71 to 80 of about 4,954 (163)

Weak ψ-Contractions on Directed Graphs with Applications to Integral Equations

Mathematics
This article deals with a few outcomes ensuring the fixed points of a weak (G,ψ)-contraction map of metric spaces comprised with a reflexive and transitive digraph G. To validate our findings, we furnish several examples. The findings we obtain enable us
Doaa Filali, Mohammad Dilshad, Mohammad Akram   +2 more
doaj   +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, Susanna Fishel, Christophe Hohlweg, Alice Mark   +3 more
wiley   +1 more source

Linkages in locally semicomplete digraphs and quasi-transitive digraphs

Discrete Mathematics, 1999
A digraph is locally semicomplete if the out-set and in-set of each vertex are semicomplete, that is, any two vertices are joined by at least one edge. A digraph is quasi-transitive if, for each path \(xyz\), the digraph contains at least one of the edges \(xz\) or \(zx\).
openaire   +2 more sources

A class of vertex-transitive digraphs, II

Journal of Combinatorial Theory, Series B, 1982
Abstract(1). We determine the number of non-isomorphic classes of self-complementary circulant digraphs with pq vertices, where p and q are distinct primes. The non-isomorphic classes of these circulant digraphs with pq vertices are enumerated. (2). We also determine the number of non-isomorphic classes of self-complementary, vertex-transitive digraphs
Chao, Chong-Yun, Wells, Jacqueline G
openaire   +2 more sources

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

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
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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

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., Gutin, G., Karimi, M., Kim, E. J., Rafiey, A.   +4 more
core   +2 more sources

k‐quasi‐transitive digraphs of large diameter

Journal of Graph Theory, 2017
AbstractGiven an integer with , a digraph is ‐quasi‐transitive if for every ‐directed path of length in , we have or (or both). In this study, we prove that if is an odd integer, , then every strong ‐quasi‐transitive digraph of diameter at least admits a partition of its vertex set such that is Hamiltonian, and both and are semicomplete ...
Jesús Alva‐Samos, César Hernández‐Cruz   +1 more
openaire   +2 more sources

A non-trivial upper bound on the threshold bias of the Oriented-cycle game

, 2016
In the Oriented-cycle game, introduced by Bollob\'as and Szab\'o, two players, called OMaker and OBreaker, alternately direct edges of $K_n$. OMaker directs exactly one edge, whereas OBreaker is allowed to direct between one and $b$ edges. OMaker wins if
Clemens, Dennis, Liebenau, Anita
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