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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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The Phylogeny Graphs of Doubly Partial Orders
Discussiones Mathematicae Graph Theory, 2013 The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced
Park Boram, Sano Yoshio
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Open-interval graphs versus closed-interval graphs
Discrete Mathematics, 1987 It is proved that a countable graph is a closed-interval graph if and only if it is an open-interval graph. A counter-example is given for uncountable graphs. Also the case of unit length intervals is studied.
Frankl, P., Maehara, H.
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A Characterization of 2-Tree Probe Interval Graphs
Discussiones Mathematicae Graph Theory, 2014 A graph is a probe interval graph if its vertices correspond to some set of intervals of the real line and can be partitioned into sets P and N so that vertices are adjacent if and only if their corresponding intervals intersect and at least one belongs ...
Brown David E. +2 more
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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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Theoretical Computer Science, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naoto Miyoshi +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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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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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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