Results 71 to 80 of about 1,056 (209)
Star Coloring Outerplanar Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2019 A proper coloring of the vertices of a graph is called a star coloring if at least three colors are used on every 4-vertex path. We show that all outerplanar bipartite graphs can be star colored using only five colors and construct the smallest known ...
Ramamurthi Radhika, Sanders Gina
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On vertex‐transitive graphs with a unique hamiltonian cycle
Journal of Graph Theory, Volume 108, Issue 1, Page 65-99, January 2025.Abstract A graph is said to be uniquely hamiltonian if it has a unique hamiltonian cycle. For a natural extension of this concept to infinite graphs, we find all uniquely hamiltonian vertex‐transitive graphs with finitely many ends, and also discuss some examples with infinitely many ends.
Babak Miraftab, Dave Witte Morris
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When the maximal graph is planar, outerplanar, and ring graph
, 2018 Let [Formula: see text] be a commutative ring with nonzero identity. Let [Formula: see text] denote the maximal graph associated to [Formula: see text], that is, [Formula: see text] is a graph with vertices as non-units of [Formula: see text], where two
Arti Sharma, Atul Gaur
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Recognizing weighted and seeded disk graphs
Journal of Computational Geometry, 2022 Disk intersection representations realize graphs by mapping vertices bijectively to disks in the plane such that two disks intersect each other if and only if the corresponding vertices are adjacent in the graph.
Boris Klemz +2 more
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On the Hub Number of Ring Graphs and Their Behavior Under Graph Operations
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This study examines the hub number of ring graphs and investigates their behavior under operations such as union, intersection, and join. Different findings for this parameter are found for a variety of types of ring graphs, such as commutative ring graphs, path ring graphs, complete ring graphs, cycle ring graphs, and star ring graphs, for which the ...
Mohammed Alsharafi +3 more
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Planar Rectilinear Drawings of Outerplanar Graphs in Linear Time
, 2020 We show how to test in linear time whether an outerplanar graph admits a planar rectilinear drawing, both if the graph has a prescribed plane embedding and if it does not.
Fabrizio Frati
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Indonesian Journal of CombinatoricsA planar graph is said to be zonal when is possible to label its vertices with the nonzero elements of ℤ3, in such a way that the sum of the labels of the vertices on the boundary of each zone is 0 in ℤ3.
Christian Barrientos, Sarah Minion
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A graph and its complement with specified properties I: connectivity
International Journal of Mathematics and Mathematical Sciences, 1979 We investigate the conditions under which both a graph G and its complement G¯ possess a specified property. In particular, we characterize all graphs G for which G and G¯ both (a) have connectivity one, (b) have line-connectivity one, (c) are 2 ...
Jin Akiyama, Frank Harary
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Strong Oriented Chromatic Number of Planar Graphs without Short Cycles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Let M be an additive abelian group. An M-strong-oriented coloring of an oriented graph G is a mapping f from V(G) to M such that f(u) j(v) whenever uv is an arc in G and f(v)−f(u) −(f(t)−f(z)) whenever uv and zt are two arcs in G.
Mickael Montassier +2 more
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Self‐avoiding walks and polygons on hyperbolic graphs
Journal of Graph Theory, Volume 106, Issue 3, Page 435-473, July 2024.Abstract We prove that for the d $d$‐regular tessellations of the hyperbolic plane by k $k$‐gons, there are exponentially more self‐avoiding walks of length n $n$ than there are self‐avoiding polygons of length n $n$. We then prove that this property implies that the self‐avoiding walk is ballistic, even on an arbitrary vertex‐transitive graph ...
Christoforos Panagiotis
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