Results 71 to 80 of about 1,282,765 (250)
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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On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords
Discussiones Mathematicae Graph Theory, 2019 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 every 1-planar graph with maximum degree ∆ ≥ 8 is edge-colorable with ∆ colors if each of its 5-cycles contains ...
Sun Lin, Wu Jianliang
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Longer Cycles in Essentially 4-Connected Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 A planar 3-connected graph G is called essentially 4-connected if, for every 3-separator S, at least one of the two components of G − S is an isolated vertex.
Fabrici Igor +3 more
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Planar Graph Isomorphism is in Log-Space
2009 24th Annual IEEE Conference on Computational Complexity, 2009 Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. There is a significant gap between extant lower and upper bounds for planar graphs as well.
Samir Datta +4 more
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DP-4-Colorability on Planar Graphs Excluding 7-Cycles Adjacent to 4- or 5-Cycles
MathematicsIn order to resolve Borodin’s Conjecture, DP-coloring was introduced in 2017 to extend the concept of list coloring. In previous works, it is proved that every planar graph without 7-cycles and butterflies is DP-4-colorable.
Fan Yang, Xiangwen Li, Ziwen Huang
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On multiplicative degree based topological indices for planar octahedron networks
Main Group Metal Chemistry, 2020 Chemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is
Dustigeer Ghulam +3 more
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On almost hypohamiltonian graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A graph $G$ is almost hypohamiltonian (a.h.) if $G$ is non-hamiltonian, there exists a vertex $w$ in $G$ such that $G - w$ is non-hamiltonian, and $G - v$ is hamiltonian for every vertex $v \ne w$ in $G$. The second author asked in [J.
Jan Goedgebeur, Carol T. Zamfirescu
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Journal of Combinatorial Theory, Series B, 1998 Given four distinct vertices in a 4-connected planar graph \(G\), we characterize when the graph \(G\) contains a \(K_4\)-subdivision with the given vertices as its degree three vertices. This result implies the following conjecture of Robertson and Thomas: a 5-connected planar graph has no \(K_4\)-subdivision with specified degree three vertices, if ...
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Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
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Computing The Irregularity Strength of Planar Graphs
Mathematics, 2018 The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network ...
Hong Yang +4 more
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