Results 61 to 70 of about 119,166 (199)
The reconstruction of outerplanar graphs
Journal of Combinatorial Theory, Series B, 1974 AbstractUlam's conjecture is that a graph G with at least three vertices can be reconstructed from the family of subgraphs of G obtained by deleting single vertices of G. This paper proves the conjecture for G outerplanar, by working first with partially labeled graphs and then applying the results obtained to the unlabeled case.
openaire +2 more sources
Planar graphs: Random walks and bipartiteness testing
Random Structures &Algorithms, Volume 55, Issue 1, Page 104-124, August 2019., 2019 We initiates the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of for graphs on n vertices. The constant‐time testability was only known for planar graphs with bounded degree. Our algorithm is based on random walks.
Artur Czumaj +3 more
wiley +1 more source
Discrete Mathematics & Theoretical Computer Science, 2004 A \emph(k,t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total order of each vertex colour class, and a (non-proper) edge k-colouring such that between each pair of colour classes no two monochromatic edges cross.
Vida Dujmović +2 more
doaj +3 more sources
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
Zero Forcing on 2-connected Outerplanar Graphs [PDF]
arXiv, 2023 We determine upper and lower bounds on the zero forcing number of 2-connected outerplanar graphs in terms of the structure of the weak dual. We show that the upper bound is always at most half the number of vertices of the graph. This work generalizes work of Hern\'andez, Ranilla and Ranilla-Cortina who proved a similar result for maximal outerplanar ...
arxiv
Feedback Arc Number and Feedback Vertex Number of Cartesian Product of Directed Cycles
Discrete Dynamics in Nature and Society, Volume 2019, Issue 1, 2019., 2019 For a digraph D, the feedback vertex number τ(D), (resp. the feedback arc number τ′(D)) is the minimum number of vertices, (resp. arcs) whose removal leaves the resultant digraph free of directed cycles. In this note, we determine τ(D) and τ′(D) for the Cartesian product of directed cycles D=Cn1→□Cn2→□…Cnk→. Actually, it is shown that τ′D=n1n2…nk∑i=1k1/
Xiaohong Chen +2 more
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
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
doaj +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
Some New Classes of Open Distance‐Pattern Uniform Graphs
International Journal of Combinatorics, Volume 2013, Issue 1, 2013., 2013 Given an arbitrary nonempty subset M of vertices in a graph G = (V, E), each vertex u in G is associated with the set fMo(u)={d(u,v) : v∈M, u≠v} and called its open M‐distance‐pattern. The graph G is called open distance‐pattern uniform (odpu‐) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u, v ∈ V(G), and M is called an open
Bibin K. Jose, Toufik Mansour
wiley +1 more source