Results 11 to 20 of about 96,525 (309)
D-magic strongly regular graphs
AKCE International Journal of Graphs and Combinatorics, 2020 For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection and a constant k such that for any vertex x, where is the D-neighbourhood set of x.
Rinovia Simanjuntak, Palton Anuwiksa
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Graphs of intersections of closed polygonal chains
Журнал Белорусского государственного университета: Математика, информатика, 2021 In the paper such subclass of string graphs as intersection graphs of closed polygonal chains (class of CPC-graphs) was considered, necessary conditions for belonging to that class, forbidden subgraphs and operations with graphs which preserve belonging ...
Nikolai P. Prochorov, Ekaterina N. Dul
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Matchings in regular graphs: minimizing the partition function [PDF]
Transactions on Combinatorics, 2021 For a graph $G$ on $v(G)$ vertices let $m_k(G)$ denote the number of matchings of size $k$, and consider the partition function $M_{G}(\lambda)=\sum_{k=0}^nm_k(G)\lambda^k$.
Márton Borbényi, Peter Csikvari
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Degrees in Link Graphs of Regular Graphs
The Electronic Journal of Combinatorics, 2022 We analyse an extremal question on the degrees of the link graphs of a finite regular graph, that is, the subgraphs induced by non-trivial spheres. We show that if $G$ is $d$-regular and connected but not complete then some link graph of $G$ has minimum degree at most $\lfloor{2d/3}\rfloor-1$, and if $G$ is sufficiently large in terms of $d$ then some ...
Benjamini, I, Haslegrave, J
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The Electronic Journal of Combinatorics, 2015 An undirected simple graph $G=(V,E)$ is called antimagic if there exists an injective function $f:E\rightarrow\{1,\dots,|E|\}$ such that $\sum_{e\in E(u)} f(e)\neq\sum_{e\in E(v)} f(e)$ for any pair of different nodes $u,v\in V$. In this note we prove — with a slight modification of an argument of Cranston et al. — that $k$-regular graphs are antimagic
Kristóf Bérczi +2 more
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Fault diagnosability of regular graphs
Theory and Applications of Graphs, 2020 An interconnection network's diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the $h$-good-neighbor conditional diagnosability, which requires ...
Mei-Mei Gu, Rong-Xia Hao, Eddie Cheng
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Regular packings of regular graphs
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amauri Gutiérrez, Anna S. Lladó
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Applications of Strongly Regular Cayley Graphs to Codebooks
IEEE Access, 2023 In this paper, we give a construction of strongly regular Cayley graphs on the finite field $\mathbb {F}_{q^{n}}$ . As applications of these strongly regular Cayley graphs, a class of codebooks is presented and proved to be asymptotically optimal with ...
Qiuyan Wang +3 more
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Formalized Mathematics, 2023 Abstract In this article regular graphs, both directed and undirected, are formalized in the Mizar system [7], [2], based on the formalization of graphs as described in [10]. The handshaking lemma is also proven.
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Signed star (k,k)-domatic number of a graph [PDF]
Opuscula Mathematica, 2014 Let \(G\) be a simple graph without isolated vertices with vertex set \(V(G)\) and edge set \(E(G)\) and let \(k\) be a positive integer. A function \(f:E(G)\longrightarrow \{-1, 1\}\) is said to be a signed star \(k\)-dominating function on \(G\) if ...
S. M. Sheikholeslami, L. Volkmann
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