Results 51 to 60 of about 161 (144)
Face Sizes and the Connectivity of the Dual
Journal of Graph Theory, Volume 110, Issue 4, Page 379-391, December 2025.ABSTRACT For each c ≥ 1, we prove tight lower bounds on face sizes that must be present to allow 1‐ or 2‐cuts in simple duals of c‐connected maps. Using these bounds, we determine the smallest genus on which a c‐connected map can have a simple dual with a 2‐cut and give lower and some upper bounds for the smallest genus on which a c‐connected map can ...
Gunnar Brinkmann +2 more
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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
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Nilpotent graphs with crosscap at most two
AKCE International Journal of Graphs and Combinatorics, 2018 Let R be a commutative ring with identity. The nilpotent graph of R, denoted by Γ N ( R ) , is a graph with vertex set Z N ( R ) ∗ , and two vertices x and y are adjacent if and only if x y is nilpotent, where Z N ( R ) = { x ∈ R : x y is nilpotent, for ...
A. Mallika, R. Kala
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A Note on the Fair Domination Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2020 For k ≥ 1, a k-fair dominating set (or just kFD-set), in a graph G is a dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V − S. The k-fair domination number of G, denoted by fdk(G), is the minimum cardinality of a kFD-set. A fair dominating
Hajian Majid, Rad Nader Jafari
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Recognizing Trees From Incomplete Decks
Journal of Graph Theory, Volume 110, Issue 3, Page 322-336, November 2025.ABSTRACT Given a graph G, the unlabeled subgraphs G − v are called the cards of G. The deck of G is the multiset { G − v : v ∈ V ( G ) }. Wendy Myrvold showed that a disconnected graph and a connected graph both on n vertices have at most ⌊ n 2 ⌋ + 1 cards in common and found (infinite) families of trees and disconnected forests for which this upper ...
Gabriëlle Zwaneveld
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Fuzzy Outerplanar Graphs and Its Applications
International Journal of Computational Intelligence SystemsThe concept of a crisp graph is essential in the study of outerplanar graphs because outerplanar graphs are a unique type of planar graphs containing special characteristics. One of the core concepts of crisp graphs, the notion of a subgraph, is utilized
Deivanai Jaisankar +3 more
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On Endomorphism Universality of Sparse Graph Classes
Journal of Graph Theory, Volume 110, Issue 2, Page 223-244, October 2025.ABSTRACT We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best‐possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by‐product,
Kolja Knauer, Gil Puig i Surroca
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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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(2,1)-Total labelling of outerplanar graphs
Discrete Applied Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Dong, Wang, Weifan
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Tight Distance Query Reconstruction for Trees and Graphs Without Long Induced Cycles
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT Given access to the vertex set V$$ V $$ of a connected graph G=(V,E)$$ G=\left(V,E\right) $$ and an oracle that given two vertices u,v∈V$$ u,v\in V $$, returns the shortest path distance between u$$ u $$ and v$$ v $$, how many queries are needed to reconstruct E$$ E $$?
Paul Bastide, Carla Groenland
wiley +1 more source