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Semipaired domination in maximal outerplanar graphs
Journal of Combinatorial Optimization, 2019Let $G$ be a graph with vertex set $V(G)$. A set $D \subseteq V(G)$ is a dominating set of $G$ if each vertex not in $D$ is adjacent to a vertex in $D$ of $G$. If $G$ has no isolated vertex, then a dominating set $S$ of $G$ is called a semi-paired dominating set of $G$ if every vertex in $S$ is paired with exactly one other vertex in $S$ that is within
Henning, Michael A. +1 more
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Farey Series and Maximal Outerplanar Graphs
SIAM Journal on Algebraic Discrete Methods, 1982Certain graphs representing Farey series of irreducible fractions are shown to be maximal outerplanar. For a suitable generalization of Farey series, the class of graphs obtained is exactly the class of maximal outerplanar graphs. Using a representation of maximal outerplanar graphs as series of irreducible fractions, efficient algorithms for deciding ...
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Convex dominating sets in maximal outerplanar graphs
Discrete Applied Mathematics, 2019In this paper, we study the concept of convex domination in maximal outerplanar graphs. For this class of graphs, we discuss several properties of this domination parameter, in particular, we provide upper bounds on the convex domination number and study effects on the convex domination number when a maximal outerplanar graph is modified by flipping a ...
Magdalena Lemańska +4 more
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Centers of maximal outerplanar graphs
Journal of Graph Theory, 1980AbstractThe center of a graph is defined to be the subgraph induced by the set of vertices that have minimum eccentricities (i.e., minimum distance to the most distant vertices). It is shown that only seven graphs can be centers of maximal outerplanar graphs.
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Connected domination in maximal outerplanar graphs
Discrete Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Isolation number of maximal outerplanar graphs
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tokunaga, Shin-ichi +2 more
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Domination and Outer Connected Domination in Maximal Outerplanar Graphs
Graphs and Combinatorics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Boundary-type sets in maximal outerplanar graphs
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Allgeier, Benjamin, Kubicki, Grzegorz
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When the maximal graph is planar, outerplanar, and ring graph
Discrete Mathematics, Algorithms and Applications, 2018Let [Formula: see text] be a commutative ring with nonzero identity. Let [Formula: see text] denote the maximal graph associated to [Formula: see text], that is, [Formula: see text] is a graph with vertices as non-units of [Formula: see text], where two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if there is ...
Sharma, Arti, Gaur, Atul
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Sombor index of maximal outerplanar graphs
Discrete Applied MathematicsLet \(G = (V(G), E(G))\) be a graph. The degree of a vertex \(v\) in \(G\) is denoted by \(d(v)\). The Somber index of the graph \(G\) is defined as \(\operatorname{SO}(G) = \sum_{xy \in E(G)} \sqrt{d^2(x) + d^2(y)}\). In this paper, the authors prove that if \(G\) is a maximal outerplanar graph of order \(n\), then \[ \operatorname{SO}(G) \geq 4(2n ...
Yunping Li, Hanyuan Deng, Zikai Tang
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