# On composition of signed graphs

K. Shahul Hameed; K.A. Germina

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 3, page 507-516
- ISSN: 2083-5892

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topK. Shahul Hameed, and K.A. Germina. "On composition of signed graphs." Discussiones Mathematicae Graph Theory 32.3 (2012): 507-516. <http://eudml.org/doc/270991>.

@article{K2012,

abstract = {A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree, namely, the difference of the number of positive and negative edges incident with a vertex. We also characterize balance in signed graph composition and have some results on the Laplacian matrices of this product.},

author = {K. Shahul Hameed, K.A. Germina},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {signed graph; eigenvalues; graph composition; regular graphs; net-regular signed graphs},

language = {eng},

number = {3},

pages = {507-516},

title = {On composition of signed graphs},

url = {http://eudml.org/doc/270991},

volume = {32},

year = {2012},

}

TY - JOUR

AU - K. Shahul Hameed

AU - K.A. Germina

TI - On composition of signed graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 3

SP - 507

EP - 516

AB - A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree, namely, the difference of the number of positive and negative edges incident with a vertex. We also characterize balance in signed graph composition and have some results on the Laplacian matrices of this product.

LA - eng

KW - signed graph; eigenvalues; graph composition; regular graphs; net-regular signed graphs

UR - http://eudml.org/doc/270991

ER -

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