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Cohen-Macaulay Circulant Graphs [PDF]
, 2012 Let G be the circulant graph C_n(S) with S a subset of {1,2,...,\lfloor n/2 \rfloor}, and let I(G) denote its the edge ideal in the ring R = k[x_1,...,x_n]. We consider the problem of determining when G is Cohen-Macaulay, i.e, R/I(G) is a Cohen-Macaulay ring.
Meulen, Kevin N. Vander +2 more
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The local vertex anti-magic coloring for certain graph operations [PDF]
HeliyonThis work proves the local vertex anti-magic coloring of even regular circulant bipartite graphs C(m;L). Let G be either Kr,r or Kr,r−F, F is a 1-factor.
L. Uma, G. Rajasekaran
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Algorithms, 2022 Recent developments in commutative algebra, linear algebra, and graph theory allow us to approach various issues in several fields. Circulant graphs now have a wider range of practical uses, including as the foundation for optical networks, discrete ...
Ahmed El-Mesady +3 more
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Integral mixed circulant graphs
Discrete Mathematics, 2023 A mixed graph is said to be \textit{integral} if all the eigenvalues of its Hermitian adjacency matrix are integer. The \textit{mixed circulant graph} $Circ(\mathbb{Z}_n,\mathcal{C})$ is a mixed graph on the vertex set $\mathbb{Z}_n$ and edge set $\{ (a,b): b-a\in \mathcal{C} \}$, where $0\not\in \mathcal{C}$.
Monu Kadyan, Bikash Bhattacharjya
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Alexandria Engineering Journal, 2022 Graph theory is a powerful and essential tool for applied scientists and engineers in analyzing and designing algorithms for several problems. Graph theory has a vital role in complex systems, especially in computer sciences. Applications of graph theory
A. El-Mesady +2 more
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Locating and Identifying Codes in Circulant Graphs
Discrete Dynamics in Nature and Society, 2021 Identifying and locating-dominating codes have been studied widely in circulant graphs. Recently, Ville Junnila et al. (Optimal bounds on codes for location in circulant graphs, Cryptography and Communications; 2019) studied identifying and locating ...
Shu Jiao Song, Weiqian Zhang, Can Xu
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The Dataset for Optimal Circulant Topologies
Big Data and Cognitive Computing, 2023 This article presents software for the synthesis of circulant graphs and the dataset obtained. An algorithm and new methods, which increase the speed of finding optimal circulant topologies, are proposed.
Aleksandr Romanov
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On the decomposition of circulant graphs using algorithmic approaches
Alexandria Engineering Journal, 2022 Many structural models in chemistry, biology, computer science, sociology, and operations research can be analyzed using graph theory. Some examples of these structure models are species movement between regions, molecular bonds, shortest spanning trees,
A. El-Mesady, Y.S. Hamed, H. Shabana
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The minimal and maximal energies of all cubic circulant graphs
AKCE International Journal of Graphs and Combinatorics, 2021 In recent article, Zhou and Zhou conjectured that among cubic circulant graphs with n vertices the maximum energy occurs whenever the largest number of components is attained.
Ilhan Hacioglu +2 more
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Layout of random circulant graphs [PDF]
Linear Algebra and its Applications, 2018 A circulant graph H is defined on the set of vertices V=\left\{ 1,\ldots,n\right\} and edges E=\left\{ \left(i,j\right):\left|i-j\right|\equiv s\left(\textrm{mod}n\right),s\in S\right\} , where S\subseteq\left\{ 1,\ldots,\lceil\frac{n-1}{2}\rceil\right\} . A random circulant graph results from deleting edges of H with probability 1-p.
Sebastian Richter, Israel Rocha
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