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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, Dalvandi Soudabeh, Heydari Farideh, Maghasedi Mohammad   +3 more
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Signed graphs with integral net Laplacian spectrum

AKCE International Journal of Graphs and Combinatorics, 2023
Given a signed graph [Formula: see text], let [Formula: see text] and [Formula: see text] be its standard adjacency matrix and the diagonal matrix of net-degrees, respectively.
M. Anđelić, T. Koledin, Z. Stanić, J. Wang   +3 more
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On signed degrees in signed graphs [PDF]

Czechoslovak Mathematical Journal, 1994
A graph is called signed if there is a designation of its edges as either positive or negative. The signed degree of a vertex \(v\) is the number of positive edges through \(v\) less the number of negative edges through \(v\). The degree sequence consists of signed degrees of all vertices in nonincreasing order.
Chartrand, Gary, Gavlas, Heather, Harary, Frank, Schultz, Michelle   +3 more
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On sign-invertible graphs

Discrete Applied Mathematics
Let $G$ be a graph and $A$ be its adjacency matrix. A graph $G$ is invertible if its adjacency matrix $A$ is invertible and the inverse of $G$ is a weighted graph with adjacency matrix $A^{-1}$. A signed graph $(G,σ)$ is a weighted graph with a special weight function $σ: E(G)\to \{-1,1\}$. A graph is sign-invertible (or sign-invertible) if its inverse
Isaiah Osborne, Dong Ye
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Projective-planar signed graphs and tangled signed graphs

Journal of Combinatorial Theory, Series B, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Orientation of Signed Graphs

European Journal of Combinatorics, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Balancing signed graphs

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 ...
Akiyama, J., Avis, D., Chvátal, V., Era, H.   +3 more
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Whole-Graph Representation Learning for the Classification of Signed Networks

IEEE Access
Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in ...
Noe Cecillon, Vincent Labatut, Richard Dufour, Nejat Arinik   +3 more
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On net-Laplacian energy of signed graphs

Communications in Combinatorics and Optimization, 2017
A signed graph is a graph where the edges are assigned either positive or negative signs‎. ‎Net degree of a signed graph is the difference between the number of positive and negative edges incident with a vertex‎. ‎It is said to be net-regular if all its
Nutan G‎. ‎Nayak
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On •-Line Signed Graphs L•(S)

Discussiones Mathematicae Graph Theory, 2015
A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}.
Sinha Deepa, Dhama Ayushi
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