# On composition of signed graphs

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

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## Abstract

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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.

## How to cite

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K. 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 -

## References

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16. [16] F. Zhang, Matrix Theory: Basic Theory and Techniques ( Springer-Verlag, 1999). Zbl0948.15001

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