Results 71 to 80 of about 3,679 (179)

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

L(h,1,1)-Labeling of Outerplanar Graphs [PDF]

Mathematical Methods of Operations Research, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CALAMONERI, Tiziana, FUSCO, EMANUELE GUIDO, Richard B. Tan, Paola Vocca   +3 more
openaire   +11 more sources

A Survey of Maximal k-Degenerate Graphs and k-Trees

Theory and Applications of Graphs
This article surveys results on maximal $k$-degenerate graphs, $k$-trees, and related classes including simple $k$-trees, $k$-paths, maximal outerplanar graphs, and Apollonian networks.
Allan Bickle
doaj   +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, Haifa Ahmed, Saad Tobaili, Ayesha Ikram   +3 more
wiley   +1 more source

On Separating Path and Tree Systems in Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science
We explore the concept of separating systems of vertex sets of graphs. A separating system of a set $X$ is a collection of subsets of $X$ such that for any pair of distinct elements in $X$, there exists a set in the separating system that contains ...
Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari, Babak Miraftab, Saeed Odak, Michiel Smid, Shakhar Smorodinsky, Yelena Yuditsky   +8 more
doaj   +1 more source

Frequent Subgraph Mining in Outerplanar Graphs [PDF]

, 2010
In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it ...
Horvath, Tamas, Ramon, Jan, Wrobel, Stefan   +2 more
core   +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

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
doaj   +1 more source

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

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, H Fraysseix, M Kurowski, MJ Bannister, P Angelini, P Bose, P Gritzmann, R Fulek, S Cabello   +8 more
core   +1 more source