Results 1 to 10 of about 34,774 (110)
Characterization of Line-Consistent Signed Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2015 The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e.
Slilaty Daniel C., Zaslavsky Thomas
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Signed analogue of line graphs and their smallest eigenvalues [PDF]
Journal of Graph Theory, 2021 AbstractIn this article, we show that every connected signed graph with smallest eigenvalue strictly greater than and large enough minimum degree is switching equivalent to a complete graph. This is a signed analogue of a theorem of Hoffman. The proof is based on what we call Hoffman's limit theorem which we formulate for Hermitian matrices, and also ...
Alexander Gavrilyuk +2 more
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Consistency in the Naturally Vertex-Signed Line Graph of a Signed Graph [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2015 A signed graph is a graph whose edges are signed. In a vertex-signed graph the vertices are signed. The latter is called consistent if the product of signs in every circle is positive. The line graph of a signed graph is naturally vertex-signed. Based on a characterization by Acharya, Acharya, and Sinha in 2009, we give constructions for the signed ...
Thomas Zaslavsky, Zaslavsky Thomas
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Discussiones Mathematicae Graph Theory, 2015 A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}.
Sinha Deepa, Dhama Ayushi
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Line Signed Graph of a Signed Total Graph
Electronic Notes in Discrete Mathematics, 2017 Abstract A signed total graph is an ordered pair T Σ ( Γ ( R ) ) : = ( T ( Γ ( R ) ) , σ ) , where T ( Γ ( R ) ) is the total graph of a commutative ring R, called the underlying graph of T Σ ( Γ ( R ) ) and T Σ ( Γ ( R ) ) is associated with a signing of its edges (a, b)
Atul Gaur, Mukti Acharya
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Eigenspaces for \(-2\) in signed line graphs
The American Journal of CombinatoricsIt is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph ...
Zoran Stanić
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Characterization of Line-Cut Signed Graphs
The National Academy of Sciences, India, 2020 A signed graph $$S=(S^u,\sigma )$$ consists of an underlying graph $$S^u$$ and a function ...
Sangita Kansal, Mukti Acharya
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On-line fault diagnosis using the signed directed graph [PDF]
Industrial & Engineering Chemistry Research, 1990 Fault diagnosis using structural knowledge, namely, the signed directed graph (SDG), is presented. A design procedure is proposed to overcome several problems associated with the SDG : it produces spurious (multiple) interpretations and it may delete the true interpretation when the process variable is going through nonsingle transition (this is ...
Chang, Chung Chien, Yu, Cheng Ching
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Characterizations of line graphs in signed and gain graphs [PDF]
European Journal of Combinatorics, 2022 We generalize three classical characterizations of line graphs to line graphs of signed and gain graphs: the Krausz's characterization, the van Rooij and Wilf's characterization and the Beineke's characterization. In particular, we present a list of forbidden gain subgraphs characterizing the class of gain-line graphs.
Matteo Cavaleri +2 more
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Star complements for ±2 in signed graphs
Special Matrices, 2022 In this article, we investigate connected signed graphs which have a connected star complement for both −2-2 and 2 (i.e. simultaneously for the two eigenvalues), where −2-2 (resp.
Mulas Raffaella, Stanić Zoran
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