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Characterization of Line-Consistent Signed Graphs
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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Homomorphisms of signed graphs
Journal of Graph Theory, 2015 International audienceA signed graph [G, Σ] 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.
Rollova, Edita +2 more
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Discrete Applied Mathematics, 2002 Define a chordally signed graph to be a signed chordal graph (meaning that each edge is designated as being positive or negative and every induced cycle is a triangle) in which every positive cycle C (meaning every cycle C that contains an even number of
Terry A. McKee, McKee, Terry A.
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Offensive Alliances in Signed Graphs
Theoretical Computer Science, 2023 Signed graphs have been introduced to enrich graph structures expressing relationships between persons or general social entities, introducing edge signs to reflect the nature of the relationship, e.g., friendship or enmity.
Qi, Xingqin +3 more
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Signed distance in signed graphs [PDF]
Linear Algebra and its Applications, 2021 Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae for the distance spectrum of some unbalanced signed graphs.
Shahul K. Hameed +4 more
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On Characterization of Balance and Consistency Preserving d-Antipodal Signed Graphs
Mathematics, 2023 A signed graph is an ordered pair Σ=(G,σ), where G is a graph and σ:E(G)⟶{+1,−1} is a mapping. For e∈E(G), σ(e) is called the sign of e and for any sub-graph H of G, σ(H)=∏e∈E(H)σ(e) is called the sign of H.
Kshittiz Chettri, Biswajit Deb
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On balance and consistency preserving 2-path signed graphs
Electronic Journal of Graph Theory and Applications, 2023 Let Σ = (G, σ) be a balanced and canonically consistent signed graph. The 2-path signed graph Σ#Σ = (G2, σ′) of Σ has the underlying graph as G2 and the sign σ′(uv) of an edge uv in it is −1 whenever in each uv-path of length 2 in Σ all edges are ...
Kshittiz Chettri +2 more
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Additively graceful signed graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Let [Formula: see text] be a signed graph of order p and size q. Let [Formula: see text] and [Formula: see text] Let [Formula: see text] be an injective function and let [Graphic: see text]gf(uv)={|f(u)−f(v)| if uv∈E+f(u)+f(v) if uv∈E−The function f is ...
Jessica Pereira +2 more
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More Equienergetic Signed Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy.
Harishchandra S. Ramane +1 more
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Ars Mathematica Contemporanea, 2022 The total graph is built by joining the graph to its line graph by means of the incidences. We introduce a similar construction for signed graphs. Under two similar definitions of the line signed graph, we define the corresponding total signed graph and we show that it is stable under switching.
Francesco Belardo +2 more
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