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The intersection graph of graded submodules of a graded module
Open Mathematics, 2022 In this article, we introduce and study the intersection graph of graded submodules of a graded module. Let MM be a left GG-graded RR-module. We define the intersection graph of GG-graded RR-submodules of MM, denoted by Γ(G,R,M)\Gamma \left(G,R,M), to be
Alraqad Tariq
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Symmetric graphs of valency seven and their basic normal quotient graphs
Open Mathematics, 2021 We characterize seven valent symmetric graphs of order 2pqn2p{q}^{n} with ...
Pan Jiangmin, Huang Junjie, Wang Chao
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On the Non-Inverse Graph of a Group
Discussiones Mathematicae - General Algebra and Applications, 2022 Let (G, *) be a finite group and S = {u ∈ G|u ≠ u−1}, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S.
Amreen Javeria, Naduvath Sudev
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Determining Number of Kneser Graphs: Exact Values and Improved Bounds [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The determining number of a graph $G = (V,E)$ is the minimum cardinality of a set $S\subseteq V$ such that pointwise stabilizer of $S$ under the action of $Aut(G)$ is trivial.
Angsuman Das, Hiranya Kishore Dey
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Remark on subgroup intersection graph of finite abelian groups
Open Mathematics, 2020 Let G be a finite group. The subgroup intersection graph Γ(G)\text{Γ}(G) of G is a graph whose vertices are non-identity elements of G and two distinct vertices x and y are adjacent if and only if |〈x〉∩〈y〉|>1|\langle x\rangle \cap \langle y\rangle
Zhao Jinxing, Deng Guixin
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Open Mathematics, 2022 Generalized Munn rings exist extensively in the theory of rings. The aim of this note is to answer when a generalized Munn ring is primitive (semiprimitive, semiprime and prime, respectively).
Guo Junying, Guo Xiaojiang
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Path homology theory of edge-colored graphs
Open Mathematics, 2021 In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau.
Muranov Yuri V., Szczepkowska Anna
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Finite groups whose intersection power graphs are toroidal and projective-planar
Open Mathematics, 2021 The intersection power graph of a finite group GG is the graph whose vertex set is GG, and two distinct vertices xx and yy are adjacent if either one of xx and yy is the identity element of GG, or ⟨x⟩∩⟨y⟩\langle x\rangle \cap \langle y\rangle is non ...
Li Huani, Ma Xuanlong, Fu Ruiqin
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Open Mathematics, 2020 A Cayley graph Γ\Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Γ\Gamma (note that the right regular representation of G is always an automorphism group of Γ ...
Pan Jiangmin
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On cospectrality of gain graphs
Special Matrices, 2022 We define GG-cospectrality of two GG-gain graphs (Γ,ψ)\left(\Gamma ,\psi ) and (Γ′,ψ′)\left(\Gamma ^{\prime} ,\psi ^{\prime} ), proving that it is a switching isomorphism invariant.
Cavaleri Matteo, Donno Alfredo
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