Results 31 to 40 of about 1,844,339 (310)
On an edge partition and root graphs of some classes of line graphs
Electronic Journal of Graph Theory and Applications, 2017 The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line ...
K Pravas, A. Vijayakumar
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On Automorphisms of Line-graphs
European Journal of Combinatorics, 1980 This paper generalizes some results on hypergraph reconstruction due to \textit{C. Berge} [C. R. Acad. Sci., Paris, Ser. A 274, 1783-1786 (1972; Zbl 0236.05129)] and \textit{J.C.Fournier} [Proc. 1rst Working Sem. Hypergraphs, Columbus 1972, Lecture Notes Math. 411, 95-98 (1974; Zbl 0302.05113)].
Zoltán Füredi, Péter L. Erdös
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Drawing Planar Graphs with Few Geometric Primitives [PDF]
, 2017 We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path ...
A Igamberdiev +13 more
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Graphoidal graphs and graphoidal digraphs: a generalization of line graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graphoidal cover of a graph G is a collection ψ of paths (not necessarily open) in G such that each path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ, and every edge of G is in exactly one path in Let
S. Arumugam, Jay S. Bagga
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Axioms, 2022 The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) for all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this note, we show that R(L(T))>n4 for any tree T of order n≥3.
Jiangfu Zhang, Baoyindureng Wu
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Morphing Planar Graph Drawings Optimally [PDF]
, 2014 We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any $n$-vertex plane graph in $O(n)$ morphing steps, thus improving upon the previously best known $O(n^2)$ upper bound.
C. Erten +10 more
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The competition number of a generalized line graph is at most two
, 2012 In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one.
Park, Boram, Sano, Yoshio
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Incidence matrices and line graphs of mixed graphs
Special Matrices, 2023 In the theory of line graphs of undirected graphs, there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, there exists no analogous result.
Abudayah Mohammad +2 more
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Biomedical Interaction Prediction with Adaptive Line Graph Contrastive Learning
Mathematics, 2023 Biomedical interaction prediction is essential for the exploration of relationships between biomedical entities. Predicted biomedical interactions can help researchers with drug discovery, disease treatment, and more.
Shilin Sun +3 more
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Journal of Combinatorial Theory, Series B, 2018 The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to determining the minimum vertex congestion of an embedding of $G$ into a tree.
Daniel J. Harvey, David R. Wood
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