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C-consistent line signed graphs of Cayley signed graphs
Journal of Interdisciplinary Mathematics, 2023The Cayley graph, signed graph and line graph are well known in the literature. Now, our focus is to study line signed graphs of Cayley signed graphs. In this paper, we have characterized the Cayley sets and generating sets for which line signed graphs of Cayley signed graphs are canonically consistent(C-consistent).
Tanuja Yadav, Amit Kumar
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Signed Circuit Cover of Bridgeless Signed Graphs
Graphs and Combinatorics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mengmeng Xie, Chuixiang Zhou
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2021
Signed graphs are another interesting variation of graphs, usually taken to be graphs in which each edge is either positive or negative. In the literature, there is more than one option for the rule for the labels on the edges of the line graph, and two of these will be considered here.
Lowell W. Beineke, Jay S. Bagga
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Signed graphs are another interesting variation of graphs, usually taken to be graphs in which each edge is either positive or negative. In the literature, there is more than one option for the rule for the labels on the edges of the line graph, and two of these will be considered here.
Lowell W. Beineke, Jay S. Bagga
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Homomorphisms of Signed Graphs
Journal of Graph Theory, 2014AbstractA signed graph is a graph G together with an assignment of signs + and − to all the edges of G where Σ is the set of negative edges. Furthermore and are considered to be equivalent if the symmetric difference of Σ1 and Σ2 is an edge cut of G. Naturally arising from matroid theory, several notions of graph theory, such as the theory of minors
Naserasr, Reza +2 more
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Packing Signatures in Signed Graphs
SIAM Journal on Discrete Mathematics, 2023A signed graph \((G,\sigma)\) is a graph \(G\) equipped with a signature \(\sigma\), which assigns to each edge of \(G\) a sign (either \(+\) or \(-\) ). A switching at a vertex \(v\) is the product of the sign of the edges incident at \(v\) with \(-1\).
Naserasr, Reza, Yu, Weiqiang
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1998
Abstract A cycle in a signed graph is a positive cycle if the number of negative edges is even and is a negative cycle if the number of negative edges is odd. A signed graph is balanced if and only if each cycle is a positive cycle, and unbalanced otherwise; equivalently, a signed graph is balanced if we can colour each vertex red or ...
Ronald C Read, Robin J Wilson
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Abstract A cycle in a signed graph is a positive cycle if the number of negative edges is even and is a negative cycle if the number of negative edges is odd. A signed graph is balanced if and only if each cycle is a positive cycle, and unbalanced otherwise; equivalently, a signed graph is balanced if we can colour each vertex red or ...
Ronald C Read, Robin J Wilson
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Journal of Dynamic Systems, Measurement, and Control, 1975
The lack of arbitrariness in the choice of bond graph sign conventions is established. It is shown that an unoriented bond graph may have no unique meaning and that with certain choices of orientation a bond graph may not correspond to any lumped parameter system constructed from the same set of elements.
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The lack of arbitrariness in the choice of bond graph sign conventions is established. It is shown that an unoriented bond graph may have no unique meaning and that with certain choices of orientation a bond graph may not correspond to any lumped parameter system constructed from the same set of elements.
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National Academy Science Letters, 2019
The square graph $$G^2$$ of a graph $$G=(V,E)$$ is a graph with same vertex set as G, and the vertices are adjacent in $$G^2$$ when their distance in G is at most two. In this paper, we characterize signed graph (or sigraph) which is a square root signed graph of some signed graph.
Deepa Sinha, Deepakshi Sharma
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The square graph $$G^2$$ of a graph $$G=(V,E)$$ is a graph with same vertex set as G, and the vertices are adjacent in $$G^2$$ when their distance in G is at most two. In this paper, we characterize signed graph (or sigraph) which is a square root signed graph of some signed graph.
Deepa Sinha, Deepakshi Sharma
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Rectangular Matrices and Signed Graphs
SIAM Journal on Algebraic Discrete Methods, 1983This paper extends the theory of graphs associated with real rectangular matrices to include information about the signs of the elements. We show when signed row and column graphs can be defined for the matrix A. We also deduce conditions under which these graphs are balanced.
Greenberg, Harvey J. +2 more
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Switched signed graphs of integer additive set-valued signed graphs
Discrete Mathematics, Algorithms and Applications, 2017Let [Formula: see text] denote a set of non-negative integers and [Formula: see text] be its power set. An integer additive set-labeling (IASL) of a graph [Formula: see text] is an injective set-valued function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text], where [Formula: see text] is the ...
Naduvath, Sudev +3 more
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