On the generalized distance spectral radius of graphs

Cui, Shu-Yu; Tian, Gui-Xian; Zheng, Lu

doi:10.48550/arxiv.1901.07695

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…In [3], upper and lower bounds for the spectral radius of the α-distance matrix were established. In [4], authors characterized the unique graph with minimum spectral radius of the α-distance matrix among the connected graphs with fixed chromatic number. In [20], a lower bound on the k-th smallest eigenvalue of the α-distance matrix was given.…”

Section: α-Spectrum Of Graphsmentioning

confidence: 99%

Bounds on the $α$-distance spectrum of graphs

Yang,

Sun,

2019

Preprint

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For a simple, undirected and connected graphis the distance matrix of G, and T r(G) is the vertex transmission diagonal matrix of G. Recently, the α-distance energy of G was defined based on the spectra of D α (G). In this paper, we define the α-distance Estrada index of G in terms of the eigenvalues of D α (G). And we give some bounds on the spectral radius of D α (G), α-distance energy and α-distance Estrada index of G.

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Section: α-Spectrum Of Graphsmentioning

confidence: 99%

Bounds on the $α$-distance spectrum of graphs

Yang,

Sun,

2019

Preprint

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“…we refer to [1,3,5,[7][8][9][10][15][16][17][18] and the references therein. For standard definitions, we refer to [6,14].…”

Section: Introductionmentioning

confidence: 99%

On spectral radius and Nordhaus-Gaddum type inequalities of the generalized distance matrix of graphs

Merajuddin

Bhatnagar²,

Pirzada³

2022

Carpathian Math. Publ.

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If $Tr(G)$ and $D(G)$ are respectively the diagonal matrix of vertex transmission degrees and distance matrix of a connected graph $G$, the generalized distance matrix $D_{\alpha}(G)$ is defined as $D_{\alpha}(G)=\alpha ~Tr(G)+(1-\alpha)~D(G)$, where $0\leq \alpha \leq 1$. If $\rho_1 \geq \rho_2 \geq \dots \geq \rho_n$ are the eigenvalues of $D_{\alpha}(G)$, the largest eigenvalue $\rho_1$ (or $\rho_{\alpha}(G)$) is called the spectral radius of the generalized distance matrix $D_{\alpha}(G)$. The generalized distance energy is defined as $E^{D_{\alpha}}(G)=\sum_{i=1}^{n}\left|\rho_i -\frac{2\alpha W(G)}{n}\right|$, where $W(G)$ is the Wiener index of $G$. In this paper, we obtain the bounds for the spectral radius $\rho_{\alpha}(G)$ and the generalized distance energy of $G$ involving Wiener index. We derive the Nordhaus-Gaddum type inequalities for the spectral radius and the generalized distance energy of $G$.

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On the generalized distance spectral radius of graphs

Cited by 2 publications

References 12 publications

Bounds on the $α$-distance spectrum of graphs

Bounds on the $α$-distance spectrum of graphs

On spectral radius and Nordhaus-Gaddum type inequalities of the generalized distance matrix of graphs

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