Results 11 to 20 of about 4,621 (198)
Edge-group choosability of outerplanar and near-outerplanar graphs [PDF]
Transactions on Combinatorics, 2020 Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$
Amir Khamseh
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The Singularity of Oriented Outerplanar Graphs with a Given Number of Inner Edges
Journal of Mathematics, 2022 A digraph is called oriented if there is at most one arc between two distinct vertices. An oriented graph is called nonsingular (singular) if its adjacency matrix AD is nonsingular (singular).
Borui He, Xianya Geng, Long Wang
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Planar, Outerplanar, and Toroidal Graphs of the Generalized Zero-Divisor Graph of Commutative Rings
Journal of Mathematics, 2021 Let A be a commutative ring with unity and let set of all zero divisors of A be denoted by ZA. An ideal ℐ of the ring A is said to be essential if it has a nonzero intersection with every nonzero ideal of A. It is denoted by ℐ≤eA.
Abdulaziz M. Alanazi +2 more
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Star Coloring Outerplanar Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2019 A proper coloring of the vertices of a graph is called a star coloring if at least three colors are used on every 4-vertex path. We show that all outerplanar bipartite graphs can be star colored using only five colors and construct the smallest known ...
Ramamurthi Radhika, Sanders Gina
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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
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Free Choosability of Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yves Aubry +2 more
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Splitting Plane Graphs to Outerplanarity
Journal of Graph Algorithms and Applications, 2023 Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard.Here we study how to minimize the number of splits to turn a plane graph ...
Gronemann, Martin +2 more
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On Another Class of Strongly Perfect Graphs
Mathematics, 2022 For a commutative ring R with unity, the associate ring graph, denoted by AG(R), is a simple graph with vertices as nonzero elements of R and two distinct vertices are adjacent if they are associates.
Neha Kansal +3 more
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Circular Separation Dimension of a Subclass of Planar Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering.
Arpitha P. Bharathi +2 more
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Minimal Cycle Bases of Outerplanar Graphs [PDF]
The Electronic Journal of Combinatorics, 1998 2-connected outerplanar graphs have a unique minimal cycle basis with length $2\vert E\vert-\vert V\vert$. They are the only Hamiltonian graphs with a cycle basis of this length.
Josef Leydold, Peter F. Stadler
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