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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 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.
I. Althöfer +4 more
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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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Edge looseness of plane graphs
Ars Mathematica Contemporanea, 2015 A face of an edge colored plane graph is called e-loose if the number of colors used on its edges is at least three. The e-looseness of a plane graph G is the minimum positive integer k such that any edge coloring of G with k colors involves an e-loose face.
J. Czap
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On d-antimagic labelings of plane graphs
Electronic Journal of Graph Theory and Applications, 2013 The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face.
Martin Baca +4 more
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Discrete Mathematics, Algorithms and ApplicationsA graph is called NIC-planar if it admits a drawing in the plane such that each edge is crossed at most once and two pairs of crossing edges share at most one vertex. A graph together with a NIC-planar drawing is a NIC-plane graph.
Zongpeng Ding
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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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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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On the edge irregularity strength for some classes of plane graphs
AIMS Mathematics, 2021 : Graph labeling is an assignment of (usually) positive integers to elements of a graph (vertices and / or edges) satisfying certain condition(s). In the last two decades, graph labeling research received much attention from researchers. This articles is
Ibrahim Tarawneh +3 more
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