1. γ-Inverse graph of some mixed graphs
- Author
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Boulahmar Wafa, Ghanem Manal, and Abudayah Mohammad
- Subjects
mixed graphs ,α-hermitian adjacency matrix ,inverse matrix ,bipartite mixed graphs ,unicyclic bipartite mixed graphs ,perfect matching ,05c20 ,05c50 ,15a30 ,Mathematics ,QA1-939 - Abstract
Let GG be a graph. Then, the inverse graph G−1{G}^{-1} of GG is defined to be a graph that has adjacency matrix similar to the inverse of the adjacency matrix of GG, where the similarity matrix is ±1\pm 1 diagonal matrix. In this article, we introduced a generalization of this definition that serves the mixed graphs where the definition applied for the α\alpha -Hermitian adjacency matrices of mixed graphs. Furthermore, for a class of unicyclic graphs, we were able to find an inverse mixed graph for a graph GG, where it was proven that G−1{G}^{-1} does not exist.
- Published
- 2024
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