γ-Inverse graph of some mixed graphs

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...

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書目詳細資料
發表在:Special Matrices
Main Authors: Boulahmar Wafa, Ghanem Manal, Abudayah Mohammad
格式: Article
語言:英语
出版: De Gruyter 2024-08-01
主題:
在線閱讀:https://doi.org/10.1515/spma-2024-0003
實物特徵
總結: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.
ISSN:2300-7451