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On the second largest distance eigenvalue of a block graph

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Abstract Bapat and Sivasubramanian [4] proved a formula for the inverse of the distance matrix of a block graph. By the result of Bapat and Sivasubramanian, we give an upper… Click to show full abstract

Abstract Bapat and Sivasubramanian [4] proved a formula for the inverse of the distance matrix of a block graph. By the result of Bapat and Sivasubramanian, we give an upper bound for the second largest distance eigenvalue of a uniform block graph. Using this, we determine all block graphs whose second largest distance eigenvalues are at most − 1 2 .

Keywords: block; second largest; distance; block graph; largest distance

Journal Title: Linear Algebra and its Applications
Year Published: 2020

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