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- W2548400417 abstract "Let M be a mixed graph and $H(M)$ be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix $R_{H}(M)=(r_{h})_{kl}$ of a mixed graph M, where $(r_{h})_{kl}=-(r_{h})_{lk}=frac{mathbf{i}}{sqrt {d_{k}d_{l}}}$ ( $mathbf{i}=sqrt{-1}$ ) if $(v_{k},v_{l})$ is an arc of M, $(r_{h})_{kl}=(r_{h})_{lk}=frac{1}{sqrt{d_{k}d_{l}}}$ if $v_{k}v_{l}$ is an undirected edge of M, and $(r_{h})_{kl}=0$ otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds on the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees." @default.
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- W2548400417 date "2017-03-03" @default.
- W2548400417 modified "2023-10-15" @default.
- W2548400417 title "Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs" @default.
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- W2548400417 doi "https://doi.org/10.1186/s13660-017-1329-8" @default.
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