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On composition of signed graphs

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Shahul Hameed K., Germina K.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 3

507-516

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Germina K.

1 Shahul Hameed K.

1 2012

Wyniki wyszukiwania

On composition of signed graphs