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- W2972742000 abstract "The eccentricity matrix $varepsilon(G)$ of a graph $G$ is obtained from the distance matrix by retaining the eccentricities (the largest distance) in each row and each column. In this paper, we give a characterization of the star graph, among the trees, in terms of invertibility of the associated eccentricity matrix. The largest eigenvalue of $varepsilon(G)$ is called the $varepsilon$-spectral radius, and the eccentricity energy (or the $varepsilon$-energy) of $G$ is the sum of the absolute values of the eigenvalues of $varepsilon(G)$. We establish some bounds for the $varepsilon$-spectral radius and characterize the extreme graphs. Two graphs are said to be $varepsilon$-equienergetic if they have the same $varepsilon$-energy. For any $n geq 5$, we construct a pair of $varepsilon$-equienergetic graphs on $n$ vertices, which are not $varepsilon$-cospectral." @default.
- W2972742000 created "2019-09-19" @default.
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- W2972742000 date "2019-09-12" @default.
- W2972742000 modified "2023-09-27" @default.
- W2972742000 title "On the spectral radius and the energy of eccentricity matrix of a graph" @default.
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