New upper bounds on the spectral radius of graphs

Maryam kargar, Tahereh Sistani

Abstract


We employ the concept of average 2-degree of the vertices and, more generally, the number of walks between two vertices to introduce new upper and lower bounds for the spectral radius and the smallest eigenvalue of a graph. We, further, show how these bounds are better than previous bounds in some cases.

Keywords


eigenvalue, spectral radius, walk, 2-degree

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