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Constructing Cospectral Non-isomorphic Signed Bipartite Graphs.
- Source :
- IAENG International Journal of Computer Science; Dec2023, Vol. 50 Issue 4, p1586-1592, 7p
- Publication Year :
- 2023
-
Abstract
- Let S = (G, σ) be a signed graph, where σ is the sign function on the edges of the underlying graph G. It is widely recognized that the adjacency spectrum alone cannot uniquely determine a signed graph. Therefore, it is of great interest to identify whether there exist any cospectral, non-isomorphic signed graphs within a specific class of signed graphs. In a significant contribution, Godsil et al. demonstrated that two components of G<subscript>1</subscript> × G<subscript>2</subscript>, where both G<subscript>1</subscript> and G<subscript>2</subscript> are connected bipartite graphs, are cospectral if and only if at the minimum one of G1 and G2 is balanced. In this paper, we first generalize Godsil’s result for two connected signed bipartite graphs S<subscript>1</subscript> and S<subscript>2</subscript>. Furthermore, we will define partitioned tensor product of two signed bipartite graphs, which will enable us to generate multiple pairs of cospectral non-isomorphic signed bipartite graphs. [ABSTRACT FROM AUTHOR]
- Subjects :
- BIPARTITE graphs
TENSOR products
Subjects
Details
- Language :
- English
- ISSN :
- 1819656X
- Volume :
- 50
- Issue :
- 4
- Database :
- Supplemental Index
- Journal :
- IAENG International Journal of Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 173982163