The bipartite Laplacian matrix of a nonsingular tree
Abstract: For a bipartite graph, the complete adjacency matrix is not necessary to display its adjacency information. In 1985, Godsil used a smaller size matrix to represent this, known as the bipartite adjacency matrix. Recently, the bipartite distance matrix of a tree with perfect matching was introduced as a concept similar to the bipartite adjacency matrix. It has been observed that these matrices are nonsingular, and a combinatorial formula for their determinants has been derived. In this article, we provide a combinatorial description of the inverse of the bipartite distance matrix and establish identities similar to some well-known identities. The study leads us to an unexpected generalization of the usual Laplacian matrix of a tree. This generalized Laplacian matrix, which we call the bipartite Laplacian matrix, is usually not symmetric, but it shares many properties with the usual Laplacian matrix. In addition, we study some of the fundamental properties of the bipartite Laplacian matrix and compare them with those of the usual Laplacian matrix.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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The bipartite Laplacian matrix of a nonsingular tree ; volume:11 ; number:1 ; year:2023 ; extent:18
Special matrices ; 11, Heft 1 (2023) (gesamt 18)
- Creator
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Bapat, Ravindra B.
Jana, Rakesh
Pati, Sukanta
- DOI
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10.1515/spma-2023-0102
- URN
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urn:nbn:de:101:1-2023082714022458555470
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:44 AM CEST
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Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Bapat, Ravindra B.
- Jana, Rakesh
- Pati, Sukanta
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