Results 11 to 20 of about 850,474 (224)
The Singularity of Oriented Outerplanar Graphs with a Given Number of Inner Edges
Journal of Mathematics, 2022 A digraph is called oriented if there is at most one arc between two distinct vertices. An oriented graph is called nonsingular (singular) if its adjacency matrix AD is nonsingular (singular).
Borui He, Xianya Geng, Long Wang
doaj +2 more sources
Equitable colorings of outerplanar graphs
Discrete Mathematics, 2002 A proper vertex coloring of a graph \(G\) is said to be equitable if the sizes of any two color classes differ by at most 1. It was conjectured by \textit{H. P. Yap} and \textit{Y. Zhang} [Bull. Inst. Math., Acad. Sin. 25, 143-149 (1997; Zbl 0882.05054)] that every outerplanar graph with maximum degree at most \(\Delta\) admits an equitable \(k ...
Alexandr Kostochka
openalex +3 more sources
Free Choosability of Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2015 A graph G is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex $$u\ne v$$u?v, the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets.
Yves Aubry +2 more
openalex +4 more sources
Pathlength of Outerplanar Graphs
, 2022 A path-decomposition of a graph G = (V, E) is a sequence of subsets of V , called bags, that satisfy some connectivity properties. The length of a path-decomposition of a graph G is the greatest distance between two vertices that belong to a same bag and the pathlength, denoted by pl(G), of G is the smallest length of its path-decompositions.
Thomas Dissaux, Nicolas Nisse
openalex +5 more sources
A Universal Point Set for 2-Outerplanar Graphs
, 2015 A point set $S \subseteq \mathbb{R}^2$ is universal for a class $\cal G$ if every graph of ${\cal G}$ has a planar straight-line embedding on $S$. It is well-known that the integer grid is a quadratic-size universal point set for planar graphs, while the
C Binucci +8 more
core +3 more sources
An O(mn2) Algorithm for Computing the Strong Geodetic Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G = (V (G), E(G)) be a graph and S be a subset of vertices of G. Let us denote by γ[u, v] a geodesic between u and v. Let Γ(S) = {γ[vi, vj] | vi, vj ∈ S} be a set of exactly |S|(|S|−1)/2 geodesics, one for each pair of distinct vertices in S.
Mezzini Mauro
doaj +2 more sources
Secure total domination number in maximal outerplanar graphs [PDF]
Discrete Applied MathematicsA subset $S$ of vertices in a graph $G$ is a secure total dominating set of $G$ if $S$ is a total dominating set of $G$ and, for each vertex $u \not\in S$, there is a vertex $v \in S$ such that $uv$ is an edge and $(S \setminus \{v\}) \cup \{u\}$ is also
Yasufumi Aita, Toru Araki
openalex +2 more sources
On the number of series parallel and outerplanar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show that the number $g_n$ of labelled series-parallel graphs on $n$ vertices is asymptotically $g_n \sim g \cdot n^{-5/2} \gamma^n n!$, where $\gamma$ and $g$ are explicit computable constants.
Manuel Bodirsky +3 more
doaj +5 more sources
Metric Dimension of Maximal Outerplanar Graphs [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 25 pages, 16 ...
M. Claverol +6 more
openaire +5 more sources