On net-Laplacian Energy of Signed Graphs

Document Type: Original paper

Author

S.S.Dempo College of Commerce and Economics, Altinho, Panaji,Goa

Abstract

A signed graph is a graph where the edges are assigned either positive or
negative signs. Net degree of a signed graph is the di erence between the number of
positive and negative edges incident with a vertex. It is said to be net-regular if all its
vertices have the same net-degree. Laplacian energy of a signed graph  is defi ned as
ε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the eigenvalues of L(Σ) and (2m)/n is
the average degree of the vertices in Σ. In this paper, we de ne net-Laplacian matrix
considering the edge signs of a signed graph and give bounds for signed net-Laplacian
eigenvalues. Further, we introduce net-Laplacian energy of a signed graph and establish
net-Laplacian energy bounds.

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