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Bipolar fuzzy outerplanar graphs approach in image shrinking [PDF]
Scientific ReportsBipolar fuzzy outerplanar graphs are interesting and significant subclasses within the broader field of fuzzy graph theory. In this paper, bipolar fuzzy outerplanar graphs, and its properties are introduced.
R Sujatha +2 more
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On the spread of outerplanar graphs [PDF]
Special Matrices, 2021 The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n ...
D. Gotshall, M. O’Brien, Michael Tait
semanticscholar +2 more sources
Isolation number of maximal outerplanar graphs
Discrete Applied Mathematics, 2019 A subset S of vertices in a graph G is called an isolating set if V ( G ) ∖ N G [ S ] is an independent set of G . The isolation number ι ( G ) is the minimum cardinality of an isolating set of G . Let G be a maximal outerplanar graph of order n with n 2
Pawaton Kaemawichanurat
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On the maximum second eigenvalue of outerplanar graphs [PDF]
Discrete Mathematics, 2023 For a fixed positive integer $k$ and a graph $G$, let $\lambda_k(G)$ denote the $k$-th largest eigenvalue of the adjacency matrix of $G$. In 2017, Tait and Tobin proved that the maximum $\lambda_1(G)$ among all outerplanar graphs on $n$ vertices is ...
George Brooks +4 more
semanticscholar +1 more source
Directed Acyclic Outerplanar Graphs Have Constant Stack Number [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2022 The stack number of a directed acyclic graph G is the minimum k for which there is a topological ordering of G and a k-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering ...
Paul Jungeblut +2 more
semanticscholar +1 more source
On the Maximum Spread of Planar and Outerplanar Graphs [PDF]
Electronic Journal of Combinatorics, 2022 The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is the ...
Zelong Li +3 more
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Outerspatial 2-Complexes: Extending the Class of Outerplanar Graphs to Three Dimensions [PDF]
Electronic Journal of Combinatorics, 2021 We introduce the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if and only if it
J. Carmesin, Tsvetomir Mihaylov
semanticscholar +1 more source
One-Bend Drawings of Outerplanar Graphs Inside Simple Polygons [PDF]
International Symposium Graph Drawing and Network Visualization, 2021 We consider the problem of drawing an outerplanar graph with $n$ vertices with at most one bend per edge if the outer face is already drawn as a simple polygon. We prove that it can be decided in $O(nm)$ time if such a drawing exists, where $m\le n-3$ is
Patrizio Angelini +4 more
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Irreducible nonmetrizable path systems in graphs
Journal of Graph Theory, Volume 102, Issue 1, Page 5-14, January 2023., 2023 Abstract A path system P ${\mathscr{P}}$ in a graph G =(V , E ) $G=(V,E)$ is a collection of paths with a unique u v $uv$ path for every two vertices u , v ∈ V $u,v\in V$. We say that P ${\mathscr{P}}$ is consistent if for any path P ∈ P $P\in {\mathscr{P}}$, every subpath of P $P$ is also in P ${\mathscr{P}}$.
Daniel Cizma, Nati Linial
wiley +1 more source
Longest and shortest cycles in random planar graphs
Random Structures &Algorithms, Volume 60, Issue 3, Page 462-505, May 2022., 2022 Abstract Let be a graph chosen uniformly at random from the class of all planar graphs on vertex set with edges. We study the cycle and block structure of when . More precisely, we determine the asymptotic order of the length of the longest and shortest cycle in in the critical range when .
Mihyun Kang, Michael Missethan
wiley +1 more source