Results 21 to 30 of about 1,772 (132)
On pathos lict graph of a tree [PDF]
, 2003 In this paper, the concept of pathos lict graph of a tree is introduced. We present a characterization of those graphs whose pathos lict graphs are planar, outerplanar, maximal outerplanar, crossing number one, eulerian and ...
Chandrasekhar, R., Muddebihal, M.H.
core +1 more source
A characterization of horizontal visibility graphs and combinatorics on words [PDF]
, 2010 An Horizontal Visibility Graph (for short, HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and ...
Gutin, Gregory +2 more
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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
Conflict-Free Coloring of Planar Graphs [PDF]
, 2017 A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors. Such colorings have applications in wireless
Abel, Zachary +7 more
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Total domination in maximal outerplanar graphs II
Discrete Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorfling, Michael +2 more
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Double-Star Isolation of Maximal Outerplanar Graphs ∗
Journal of Physics: Conference Series, 2023 Abstract In the graph G = (V, E), V represents the set of vertices and E represents the set of edges. ℱ represents a family of graphs. A subset S ⊆ V is considered an ℱ -isolating set if G[V\NG[S]] does not contain F as a subgraph for all F ∈ ℱ.
Jingdong Cao +3 more
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A Note on Edge‐Group Choosability of Planar Graphs without 5‐Cycles
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 This paper is devoted to a study of the concept of edge‐group choosability of graphs. We say that G is edge‐k‐group choosable if its line graph is k‐group choosable. In this paper, we study an edge‐group choosability version of Vizing conjecture for planar graphs without 5‐cycles and for planar graphs without noninduced 5‐cycles (2010 Mathematics ...
Amir Khamseh, Andrei V. Kelarev
wiley +1 more source
Drawing Planar Graphs with Few Geometric Primitives [PDF]
, 2017 We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path ...
A Igamberdiev +13 more
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Nonplanarity of Iterated Line Graphs
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 The 1‐crossing index of a graph G is the smallest integer k such that the kth iterated line graph of G has crossing number greater than 1. In this paper, we show that the 1‐crossing index of a graph is either infinite or it is at most 5. Moreover, we give a full characterization of all graphs with respect to their 1‐crossing index.
Jing Wang, Alfred Peris
wiley +1 more source
On Separating Path and Tree Systems in Graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe 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 +8 more
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