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Discrete Mathematics, 1985 The interval thickness of a graph G is the minimum clique number of all the interval supergraphs of G. The clique number of a graph is the number of nodes of its biggest complete subgraph. On the other hand, the node- search number is the least number of searchers (pebbles) required to clear the ''contaminated'' edges of a graph. A contaminated edge is
Lefteris M. Kirousis +3 more
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The Cost of Global Broadcast in Dynamic Radio Networks [PDF]
, 2016 We study the single-message broadcast problem in dynamic radio networks. We show that the time complexity of the problem depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary ...
Ahmadi, Mohamad +3 more
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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
Discussiones Mathematicae Graph Theory, 2017 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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Mathematics, 2019 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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Counting interval graphs [PDF]
Transactions of the American Mathematical Society, 1982 In this paper we enumerate interval graphs (up to isomorphism) along with labelled interval graphs, identity interval graphs, transitive interval graphs and various sorts of unit interval graphs. The enumeration makes use of a structural decomposition of interval graphs which leads to a characterization of those interval graphs having a unique interval
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Discrete Applied Mathematics, 1998 If \(S\) is a subset of the vertex set of a connected graph \(G\), then the Steiner distance \(d(S)\) of \(S\) is the minimum number of edges of a connected subgraph of \(G\) that contains \(S\); this subgraph is always a tree and is called a Steiner tree for \(S\). The Steiner interval \(I(S)\) of \(S\) is the set of all vertices of \(G\) which lie in
Ewa Kubicka +2 more
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End Simplicial Vertices in Path Graphs
Discussiones Mathematicae Graph Theory, 2016 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]
Discrete Mathematics & Theoretical Computer ScienceA 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 Sets and Systems, 2021 : 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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On the Representation of a PI-Graph
Trends in Computational and Applied Mathematics, 2007 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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