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On derived t-path, t=2,3 signed graph and t-distance signed graph
MethodsXA signed graph Σ is a pair Σ=(Σu,σ)that consists of a graph (Σu,E) and a sign mapping called signature σ from E to the sign group {+,−}. In this paper, we discuss the t-path product signed graph (Σ)^twhere vertex set of (Σ)^t is the same as that of Σ and
Deepa Sinha, Sachin Somra
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Total graph of a signed graph [PDF]
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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Algorithmic approach to find S-consistency in Common-Edge signed graph
MethodsX, 2022 Common-Edge signed graph CE(S) of a signed graph S is a signed graph whose vertex-set is the pairs of adjacent edges in S and two vertices are adjacent if the corresponding pairs of adjacent edges of S have exactly one edge in common, with the sign same ...
Anshu Sethi +2 more
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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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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
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Signed graphs and signed cycles of hyperoctahedral groups
Electronic Journal of Graph Theory and Applications, 2023 For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices.
Ryo Uchiumi
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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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Discrete Applied Mathematics, 1982 AbstractA signed graph is a graph with a sign attached to each arc. This article introduces the matroids of signed graphs, which generalize both the polygon matroids and the even-circle (or unoriented cycle) matroids of ordinary graphs. The concepts of balance, switching, restriction and contraction, double covering graphs, and linear representation of
Ebrahim Ghorbani +3 more
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Negative (and positive) circles in signed graphs: A problem collection
AKCE International Journal of Graphs and Combinatorics, 2018 A signed graph is a graph whose edges are labeled positive or negative. The sign of a circle (cycle, circuit) is the product of the signs of its edges. Most of the essential properties of a signed graph depend on the signs of its circles. Here I describe
Thomas Zaslavsky
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Signed graphs connected with the root lattice
Bibechana, 2014 For any base of the root lattice (An) we can construct a signed graph. A signed graph is one whose edges are signed by +1 or -1. A signed graph is balanced if and only if its vertex set can be divided into two sets-either of which may be empty–so that ...
RN Yadav
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