Results 71 to 80 of about 1,353,416 (150)
Forcing (G,D)-number of a Graph [PDF]
, 2011 By a graph G=(V,E), we mean a finite, undirected connected graph without loops and multiple ...
Nagarajan, A. +3 more
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A Note On Vertex Colorings Of Plane Graphs
Discussiones Mathematicae Graph Theory, 2014 Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V , let c(v) denote the sum of the weight of v ∈ V and of the weights of all edges and all faces incident with v.
Fabricia Igor +2 more
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, 2009 For standard terminology and notion in graph theory we refer the reader to Harary [7]; the non-standard will be given in this paper as and when required.
Reddy, P. Siva Kota +3 more
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A note on face coloring entire weightings of plane graphs
Discussiones Mathematicae Graph Theory, 2014 Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _.
Jendrol Stanislav, Šugerek Peter
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New Results of Face Labeling for Some Plane Graphs
IEEE Access, 2019 A labeling of a plane graph is called super d-antimagic if the vertices receive the smallest labels and the weight set of all faces in an arithematic progression with difference d, where weight of each face is the some of all labels correspond to that ...
Nabila Hameed +4 more
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On the Weight of Minor Faces in Triangle-Free 3-Polytopes
Discussiones Mathematicae Graph Theory, 2016 The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or ...
Borodin Oleg V., Ivanova Anna O.
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WORM Colorings of Planar Graphs
Discussiones Mathematicae Graph Theory, 2017 Given three planar graphs F,H, and G, an (F,H)-WORM coloring of G is a vertex coloring such that no subgraph isomorphic to F is rainbow and no subgraph isomorphic to H is monochromatic. If G has at least one (F,H)-WORM coloring, then W−F,H(G) denotes the
Czap J., Jendrol’ S., Valiska J.
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Facial [r,s,t]-Colorings of Plane Graphs
Discussiones Mathematicae Graph Theory, 2019 Let G be a plane graph. Two edges are facially adjacent in G if they are consecutive edges on the boundary walk of a face of G. Given nonnegative integers r, s, and t, a facial [r, s, t]-coloring of a plane graph G = (V,E) is a mapping f : V ∪ E → {1, . .
Czap Július +3 more
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An Extension of Kotzig’s Theorem
Discussiones Mathematicae Graph Theory, 2016 In 1955, Kotzig proved that every 3-connected planar graph has an edge with the degree sum of its end vertices at most 13, which is tight. An edge uv is of type (i, j) if d(u) ≤ i and d(v) ≤ j.
Aksenov Valerii A. +2 more
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Map Generalization as a Graph Drawing Problem
, 1995 A map may be regarded as a plane graph drawing; and, with the growth of the field of computer cartography, a map is increasingly treated as a straight-line plane graph drawing.
Alan Saalfeld, Saalfeld, Alan
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