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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring
Immel Poppy, Wenger Paul S.
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Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG
Naeem Jan +6 more
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End Simplicial Vertices in Path Graphs
A graph is a path graph if there is a tree, called UV -model, whose vertices are the maximal cliques of the graph and for each vertex x of the graph the set of maximal cliques that contains it induces a path in the tree.
Gutierrez Marisa, Tondato Silvia B.
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On Generalizations of Pairwise Compatibility Graphs [PDF]
A graph $G$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree and an interval $I$, such that each leaf of the tree is a vertex of the graph, and there is an edge $\{ x, y \}$ in $G$ if and only if the weight of the path in the
Tiziana Calamoneri +3 more
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Novel Concept of Interval-Valued Neutrosophic Incidence Graphs with Application [PDF]
: Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event are described based on three possible aspects, i.e., the membership degree, neutral membership degree and non-membership degree.
Siti Nurul Fitriah Mohamad +4 more
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Betweenness in graphs: A short survey on shortest and induced path betweenness
Betweenness is a universal notion present in several disciplines of mathematics. The notion of betweenness has a profound history and many pioneers like Euclid, Pasch, Hilbert have studied betweenness axiomatically.
Manoj Changat +2 more
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On the Representation of a PI-Graph
Consider two parallel lines (denoted r1 and r2). A graph is a PI graph (Point-Interval graph) if it is an intersection graph of a family F of triangles between r1 and r2 such that each triangle has an interval with two endpoints on r1 and a vertex (a ...
S.M. Almeida, C.P. de Mello, A. Gomide
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fred R. McMorris +2 more
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Interval-valued bipolar fuzzy line graphs
Objectives The notion of Bipolarity based on positive and negative outcomes. It is well known that bipolar models give more precision, flexibility, and compatibility to the system as compared to the classical models and fuzzy models.
Keneni Abera Tola +2 more
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Cliques and Clique Covers in Interval-Valued Fuzzy Graphs
Finding cliques and clique covers in graphs are one of the most needful tasks. In this paper, interval-valued fuzzy cliques (IVFQs) and interval-valued fuzzy clique covers (IVFQCs) of an interval-valued fuzzy graph (IVFG) are introduced by introducing ...
Napur Patra +3 more
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