Results 51 to 60 of about 2,598,126 (331)
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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European Journal of Combinatorics, 1991 A graph with signed arcs is oriented by directing each end of each arc in accordance with a sign-compatibility rule. We prove that the regions of the hyperplane representation of a signed graph ∑, as well as the vertices of the convex hull of all degree vectors of orientations of ∑, are in natural one-to-one correspondence with the cyclic orientations ...
Thomas Zaslavsky, Thomas Zaslavsky
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The Wiener index of signed graphs [PDF]
Applied Mathematics and Computation, 2022 The Wiener index of a graph $W(G)$ is a well studied topological index for graphs. An outstanding problem of olt{ }s is to find graphs $G$ such that $W(G)=W(G-v)$ for all vertices $v\in V(G)$, with the only known example being $G=C_{11}$. We relax this problem by defining a notion of Wiener indices for signed graphs, which we denote by $W_ (G ...
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Six signed Petersen graphs, and their automorphisms [PDF]
, 2012 Up to switching isomorphism there are six ways to put signs on the edges of the Petersen graph. We prove this by computing switching invariants, especially frustration indices and frustration numbers, switching automorphism groups, chromatic numbers, and
Zaslavsky, Thomas
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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 ...
Hiroshi Era +3 more
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Signed degree sequences of signed graphs [PDF]
Journal of Graph Theory, 1997 This paper gives necessary and sufficient conditions for an integral sequence to be the signed degree sequence of a signed graph or a signed tree, answering a question raised by Chartrand et al. (1994). (G. Chartrand, H. Gavlas, F. Harary, and M. Schultz, On signed degrees in signed graphs, Czech. Math. J. 44 (1994), 677–690).
David Kuo +3 more
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Constructing cospectral signed graphs [PDF]
Linear and Multilinear Algebra, 2019 13 pages, 4 ...
Francesco Belardo +3 more
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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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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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