The distance-regular graphs such that all of its second largest local eigenvalues are at most one
classification
🧮 math.CO
keywords
distance-regulareigenvalueeigenvaluesgraphgraphslargestlocalsecond
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In this paper, we classify distance regular graphs such that all of its second largest local eigenvalues are at most one. Also we discuss the consequences for the smallest eigenvalue of a distance-regular graph. These extend a result by the first author, who classified the distance-regular graph with smallest eigenvalue $-1-\frac{b_1}{2}$.
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