Results 11 to 20 of about 1,002 (213)
Orientable -distance magic regular graphs
AKCE International Journal of Graphs and Combinatorics, 2021 Hefetz, Mütze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation (Hefetz et al., 2010). In this paper we support the analogous question for distance magic labeling. Let be an Abelian group of order .
Paweł Dyrlaga, Karolina Szopa
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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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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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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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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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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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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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Regular Partitions of Regular Graphs [PDF]
Canadian Mathematical Bulletin, 1978 In the study of the combinatorial structure of edge-graphs of convex polytopes one may ask whether a given graph possesses a partition consisting of certain kinds of subgraphs.In this paper we describe some special partitions of 3-valent and 4-valent graphs.
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