DOI: 10.29007/fqlw
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Adjacency Matrix of Product of Graphs

Abstract: In graph theory, different types of matrices associated with graph, e.g. Adjacency matrix, Incidence matrix, Laplacian matrix etc. Among all adjacency matrix play an important role in graph theory. Many products of two graphs as well as its generalized form had been studied, e.g., cartesian product, 2−cartesian product, tensor product, 2−tensor product etc. In this paper, we discuss the adjacency matrix of two new product of graphs G H, where = ⊗2, ×2. Also, we obtain the spectrum of these products of graphs.

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“…Consequently, to explicitly address real clinical problems and learn from the imperfect unaligned target images, our proposed method optimizes the structural learning for noncontrast CT attenuation reconstruction by exploring the equilibrium of the loss computation between the structure reconstruction from contrastenhanced CT and noncontrast CT attenuation. Inspired by the adjacency matrix (Acharya and Mehta, 2020) in graph convolutional networks (GCNs), the adjacency content-transfer approach learns the maximal gradient ratio of the absolute difference from the adjacency matrix. By exploiting our network, we were able to obtain a similar result that is as robust as those reported by previous studies (Koike et al 2020, Liugang et al 2020.…”
Section: Discussionmentioning
confidence: 99%
“…Consequently, to explicitly address real clinical problems and learn from the imperfect unaligned target images, our proposed method optimizes the structural learning for noncontrast CT attenuation reconstruction by exploring the equilibrium of the loss computation between the structure reconstruction from contrastenhanced CT and noncontrast CT attenuation. Inspired by the adjacency matrix (Acharya and Mehta, 2020) in graph convolutional networks (GCNs), the adjacency content-transfer approach learns the maximal gradient ratio of the absolute difference from the adjacency matrix. By exploiting our network, we were able to obtain a similar result that is as robust as those reported by previous studies (Koike et al 2020, Liugang et al 2020.…”
Section: Discussionmentioning
confidence: 99%