Bapat, R. B. ; Kalita, D. ; Pati, S. (2012) On weighted directed graphs Linear Algebra and its Applications, 436 (1). pp. 99-111. ISSN 0024-3795
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Official URL: http://www.sciencedirect.com/science/article/pii/S...
Related URL: http://dx.doi.org/10.1016/j.laa.2011.06.035
Abstract
The study of a mixed graph and its Laplacian matrix have gained quite a bit of interest among the researchers. Mixed graphs are very important for the study of graph theory as they provide a setup where one can have directed and undirected edges in the graph. In this article we present a more general structure, namely the weighted directed graphs and supply appropriate generalizations of several existing results for mixed graphs related to singularity of the corresponding Laplacian matrix. We also prove many new combinatorial results relating the Laplacian matrix and the graph structure.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Laplacian Matrix; Mixed Graph; Weighted Directed Graph; 3-colored Digraph; Edge Singularity |
| ID Code: | 81598 |
| Deposited On: | 07 Feb 2012 05:14 |
| Last Modified: | 07 Feb 2012 05:14 |
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