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On $bullet$-lict signed graphs $L_{bullet_c}(S)$ and $bullet$-line signed graphs $L_bullet(S)$ [PDF]
Transactions on Combinatorics, 2016 A emph{signed graph} (or, in short, emph{sigraph}) $S=(S^u,sigma)$ consists of an underlying graph $S^u :=G=(V,E)$ and a function $sigma:E(S^u)longrightarrow {+,-}$, called the signature of $S$. A emph{marking} of $S$ is a function $mu:V(S)longrightarrow
Mukti Acharya +2 more
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Further Results on the Nullity of Signed Graphs
Journal of Applied Mathematics, 2014 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and
Yu Liu, Lihua You
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Signed Complete Graphs with Maximum Index
Discussiones Mathematicae Graph Theory, 2020 Let Γ = (G, σ) be a signed graph, where G is the underlying simple graph and σ E(G) → {−, +} is the sign function on the edges of G. The adjacency matrix of a signed graph has −1 or +1 for adjacent vertices, depending on the sign of the edges.
Akbari Saieed +3 more
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Notes on upper bounds for the largest eigenvalue based on edge-decompositions of a signed graph
Kuwait Journal of Science, 2023 The adjacency matrix of a signed graph has +1 or -1 for adjacent vertices, depending on the sign of the connecting edge. According to this concept, an ordinary graph can be interpreted as a signed graph without negative edges.
Zoran Stanić
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Discrete Applied Mathematics, 1981 AbstractA signed graph based on F is an ordinary graph F with each edge marked as positive or negative. Such a graph is called balanced if each of its cycles includes an even number of negative edges. Psychologists are sometimes interested in the smallest number d=d(G) such that a signed graph G may be converted into a balanced graph by changing the ...
Jin Akiyama +3 more
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Improved kernels for Signed Max Cut parameterized above lower bound on (r,l)-graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A graph $G$ is signed if each edge is assigned $+$ or $-$. A signed graph is balanced if there is a bipartition of its vertex set such that an edge has sign $-$ if and only if its endpoints are in different parts.
Luerbio Faria +3 more
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Ain Shams Engineering JournalThis paper presents an algorithm to compute the integrity of a signed fuzzy graph by systematically evaluating vertex subsets, removing them, and analyzing the resulting connected components.
Chakaravarthy Sankar +3 more
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On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs
Discussiones Mathematicae Graph Theory, 2022 A signed graph has edge weights drawn from the set {+1, −1}, and is sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is sign-unbalanced.
Bašić Nino +3 more
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A Note on the Maximum Genus of Graphs with Diameter 4 [PDF]
, 2007 Let G be a simple graph with diameter four, if G does not contain complete subgraph K3 of order ...
WeiLi, He, Xiang, Ren, Lin, Zhao
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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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