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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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Product Signed Domination in Graphs
Ratio Mathematica, 2022 Let be a simple graph. The closed neighborhood of , denoted by , is the set . A function is a product signed dominating function, if for every vertex where . The weight of , denoted by , is the sum of the function values of all the vertices in . .
T M Velammal, A Nagarajan, K Palani
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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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Homomorphisms of planar signed graphs to signed projective cubes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1.
Reza Naserasr +2 more
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Star complements in signed graphs with two symmetric eigenvalues
Kuwait Journal of Science, 2022 We consider signed graphs $G$ whose spectrum is comprised of exactly two (distinct) eigenvalues that differ only in sign, abbreviated to signed graphs with two symmetric eigenvalues. We obtain some relationships between such signed graphs and their star
Assoc. Prof, Zoran Stanić
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More on signed graphs with at most three eigenvalues [PDF]
, 2021 We consider signed graphs with just 2 or 3 distinct eigenvalues, in particular (i) those with at least one simple eigenvalue, and (ii) those with vertexdeleted subgraphs which themselves have at most 3 distinct eigenvalues. We also construct new examples
StaniĆ, Zoran +4 more
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