Results 1 to 10 of about 1,010 (104)
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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Veterinary Dermatology, Volume 33, Issue 1, Page 17-e6, February 2022., 2022 Background – Because of the increased incidence of multidrug‐resistant (MDR) bacteria, the use of disinfectants over antibiotics has been encouraged. However, the interactions between disinfectants and host local immunity are poorly understood. Objective – To assess the effects of chlorhexidine digluconate (Chx), with and without selected host defence ...
Domenico Santoro +3 more
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On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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An Analogue of DP-Coloring for Variable Degeneracy and its Applications
Discussiones Mathematicae Graph Theory, 2022 A graph G is list vertex k-arborable if for every k-assignment L, one can choose f(v) ∈ L(v) for each vertex v so that vertices with the same color induce a forest. In [6], Borodin and Ivanova proved that every planar graph without 4-cycles adjacent to 3-
Sittitrai Pongpat, Nakprasit Kittikorn
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On (p, 1)-Total Labelling of Some 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
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Cyclic Permutations in Determining Crossing Numbers
Discussiones Mathematicae Graph Theory, 2022 The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied.
Klešč Marián, Staš Michal
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Colorings of Plane Graphs Without Long Monochromatic Facial Paths
Discussiones Mathematicae Graph Theory, 2021 Let G be a plane graph. A facial path of G is a subpath of the boundary walk of a face of G. We prove that each plane graph admits a 3-coloring (a 2-coloring) such that every monochromatic facial path has at most 3 vertices (at most 4 vertices).
Czap Július +2 more
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The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
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Rotor-Routing Induces the Only Consistent Sandpile Torsor Structure on Plane Graphs
Forum of Mathematics, Sigma, 2023 We make precise and prove a conjecture of Klivans about actions of the sandpile group on spanning trees. More specifically, the conjecture states that there exists a unique ‘suitably nice’ sandpile torsor structure on plane graphs which is induced by ...
Ankan Ganguly, Alex McDonough
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Untwisting 3‐strand torus knots
Bulletin of the London Mathematical Society, Volume 52, Issue 3, Page 429-436, June 2020., 2020 Abstract We prove that the signature bound for the topological 4‐genus of 3‐strand torus knots is sharp, using McCoy's twisting method. We also show that the bound is off by at most 1 for 4‐strand and 6‐strand torus knots, and improve the upper bound on the asymptotic ratio between the topological 4‐genus and the Seifert genus of torus knots from 2/3 ...
S. Baader, I. Banfield, L. Lewark
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