On weighted directed graphs

By Ravindra B. Bapat, D. Kalita, S. Pati. 2012

82 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f51297c99ccad01ca3bcbf46222f61a250e50468

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In Computational Theory and Mathematics

1. Aniruddha Samanta
2. Ranjit Mehatari
3. M. Rajesh Kannan

In Geometry and Topology

1. Aniruddha Samanta
2. Ranjit Mehatari
3. M. Rajesh Kannan

Citations in the corpus

• On the adjacency matrix of a complex unit gain graph (2018, background): “Particular cases of the notion of adjacencymatrix ofT-gain graphswere consideredwith different weights in the literature [9,10].”