Results 61 to 70 of about 211 (163)
The Degree-Diameter Problem for Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2017 For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that nΔ,D=ΔD2+O (ΔD2−1)$n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D \over 2 ...
Dankelmann Peter +2 more
doaj +1 more source
Outerplanar Partitions of Planar Graphs
Journal of Combinatorial Theory, Series B, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
Algorithm-based radio labeling for optimal channel assignment in outerplanar graphs
Frontiers in Computer ScienceIntroductionRadio labeling of graphs extends the channel assignment problem by assigning non-negative integers to vertices of a connected graph G such that |h(℘)−h(𝓆)|≥diam(ℊ)+1−d(℘, 𝓆).
Baskar Mari, Ravi Sankar Jeyaraj
doaj +1 more source
Four-searchable biconnected outerplanar graphs
Discrete Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diner, Oznur Yasar +3 more
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Random graphs embeddable in order‐dependent surfaces
Random Structures &Algorithms, Volume 64, Issue 4, Page 940-985, July 2024.Abstract Given a ‘genus function’ g=g(n)$$ g=g(n) $$, we let Eg$$ {\mathcal{E}}^g $$ be the class of all graphs G$$ G $$ such that if G$$ G $$ has order n$$ n $$ (i.e., has n$$ n $$ vertices) then it is embeddable in a surface of Euler genus at most g(n)$$ g(n) $$.
Colin McDiarmid, Sophia Saller
wiley +1 more source
On Vertices Enforcing a Hamiltonian Cycle
Discussiones Mathematicae Graph Theory, 2013 A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian.
Fabrici Igor +2 more
doaj +1 more source
On tree decompositions whose trees are minors
Journal of Graph Theory, Volume 106, Issue 2, Page 296-306, June 2024.Abstract In 2019, Dvořák asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$.
Pablo Blanco +5 more
wiley +1 more source