Results 61 to 70 of about 584,165 (157)
Area-Efficient Drawings of Outerplanar Graphs
, 2004 We show that an outerplanar graph G with n vertices and degree d admits a planar straight-line grid drawing with area O(dn^{1.48}) in O(n) time.
Ashim Garg +3 more
core +1 more source
Planar embeddability of the vertices of a graph using a fixed point set is NP-hard
Journal of Graph Algorithms and Applications, 2006 Let G=(V,E) be a graph with n vertices and let P be a set of n points in the plane. We show that deciding whether there is a planar straight-line embedding of G such that the vertices V are embedded onto the points P is NP-complete, even when G is 2 ...
Sergio Cabello
doaj +1 more source
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 +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
On the Relationships between Zero Forcing Numbers and Certain Graph Coverings
Special Matrices, 2014 The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all ...
Taklimi Fatemeh Alinaghipour +2 more
doaj +1 more source
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
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
Simultaneous Graph Embedding with Bends and Circular Arcs
, 2007 We consider the problem of simultaneous embedding of planar graphs. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar ...
Cappos, Justin +3 more
core +1 more source