TY - JOUR
ID - 13578
TI - On net-Laplacian Energy of Signed Graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Nayak, Nutan G.
AD - S.S.Dempo College of Commerce and Economics, Altinho, Panaji,Goa
Y1 - 2017
PY - 2017
VL - 2
IS - 1
SP - 11
EP - 19
KW - Net-regular signed graph
KW - net-Laplacian matrix
KW - net-Laplacian energy
DO - 10.22049/cco.2017.13578
N2 - 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 vertices have the same net-degree. Laplacian energy of a signed graph $Sigma$ is defined as $varepsilon({L} Sigma)) = sum_{i=1}^{n}|gamma_i - frac{2m}{n}|$ where $gamma_{1}, gamma _{2} ,ldots, gamma_{n}$ are the eigenvalues of $L(Sigma)$ and $frac{2m}{n}$ is the average degree of the vertices in $Sigma$. In this paper, we define 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13578.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13578_7e090ec81543bab5c2a566524067cc39.pdf
ER -