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Facial Rainbow Coloring of Plane Graphs
Discussiones Mathematicae Graph Theory, 2019 A vertex coloring of a plane graph G is a facial rainbow coloring if any two vertices of G connected by a facial path have distinct colors. The facial rainbow number of a plane graph G, denoted by rb(G), is the minimum number of colors that are necessary
Jendroľ Stanislav, Kekeňáková Lucia
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Unique-Maximum Coloring Of Plane Graphs
Discussiones Mathematicae Graph Theory, 2016 A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . . . , k so that, for each face of G, the maximum color occurs exactly once on the vertices of α.
Fabrici Igor, Göring Frank
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On Noncrossing and Plane Tree-Like Structures
Communications in Advanced Mathematical Sciences, 2021 Mathematical trees are connected graphs without cycles, loops and multiple edges. Various trees such as Cayley trees, plane trees, binary trees, $d$-ary trees, noncrossing trees among others have been studied extensively.
Isaac Owino Okoth
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Splitting Plane Graphs to Outerplanarity
Journal of Graph Algorithms and Applications, 2023 Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard.Here we study how to minimize the number of splits to turn a plane graph ...
Gronemann, Martin +2 more
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Folding Equilateral Plane Graphs [PDF]
International Journal of Computational Geometry & Applications, 2011 We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical configuration. By contrast, it is known that such reconfiguration is not always possible for linear (nonequilateral) trees and for (nonlinear ...
Abel, Zachary Ryan +6 more
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On Face Irregular Evaluations of Plane Graphs
Discussiones Mathematicae Graph Theory, 2022 We investigate face irregular labelings of plane graphs and we introduce new graph characteristics, namely face irregularity strength of type (α,β,γ). We obtain some estimation on these parameters and determine the precise values for certain families of ...
Bača Martin +3 more
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Ars Mathematica Contemporanea, 2015 Summary: A plane graph is called alternating if all adjacent vertices have different degrees, and all neighboring faces as well. Alternating plane graphs were introduced in 2008. This paper presents the previous research on alternating plane graphs.{ }There are two smallest alternating plane graphs, having 17 vertices and 17 faces each.
Althöfer, Ingo +4 more
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Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)
Journal of Mathematics, 2021 In this study, we used grids and wheel graphs G=V,E,F, which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set.
Aleem Mughal, Noshad Jamil
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Strong parity vertex coloring of plane graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A strong parity vertex coloring of a 2-connected plane graph is a coloring of the vertices such that every face is incident with zero or an odd number of vertices of each color.
Tomas Kaiser +3 more
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Affine Graphs and their Topological Indices
Journal of Mathematics, 2021 Graphs are essential tools to illustrate relationships in given datasets visually. Therefore, generating graphs from another concept is very useful to understand it comprehensively. This paper will introduce a new yet simple method to obtain a graph from
Abdurrahman Dayioglu
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