Results 11 to 20 of about 170,454 (272)
Kramers–Wannier Duality and Random-Bond Ising Model [PDF]
EntropyWe present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators ...
Chaoming Song
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Equitable Coloring of IC-Planar Graphs with Girth g ≥ 7
Axioms, 2023 An equitable k-coloring of a graph G is a proper vertex coloring such that the size of any two color classes differ at most 1. If there is an equitable k-coloring of G, then the graph G is said to be equitably k-colorable.
Danjun Huang, Xianxi Wu
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Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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A note on nearly Platonic graphs with connectivity one
Electronic Journal of Graph Theory and Applications, 2021 A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek,
Dalibor Froncek +3 more
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Advanced Engineering Materials, EarlyView., 2023 The study presents the mechanical and in situ sensing performance of digital light processing‐enabled 2D lattice nanocomposites under monotonic tensile and repeated cyclic loading, and provides guidelines for the design of architectures suitable for strain sensors and smart lightweight structures.
Omar Waqas Saadi +3 more
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An improved upper bound for the dynamic list coloring of 1-planar graphs
AIMS Mathematics, 2022 A graph is 1-planar if it can be drawn in the plane such that each of its edges is crossed at most once. A dynamic coloring of a graph G is a proper vertex coloring such that for each vertex of degree at least 2, its neighbors receive at least two ...
Xiaoxue Hu, Jiangxu Kong
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Computational Study on a PTAS for Planar Dominating Set Problem
Algorithms, 2013 The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time ...
Qian-Ping Gu, Marjan Marzban
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On certain prime cordial families of graphs
Journal of Taibah University for Science, 2020 Graph labelling is an important tool in modelling real life problems. In the present paper, different graph families are studied for prime cordial labelling.
Nazeran Idrees +3 more
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Total Coloring of Dumbbell Maximal Planar Graphs
Mathematics, 2022 The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+2)-colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC holds for dumbbell maximal planar graphs.
Yangyang Zhou +3 more
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On Longest Cycles in Essentially 4-Connected Planar Graphs
Discussiones Mathematicae Graph Theory, 2016 A planar 3-connected graph G is essentially 4-connected if, for any 3-separator S of G, one component of the graph obtained from G by removing S is a single vertex.
Fabrici Igor +2 more
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