Non-Bipartite Distance-Regular Graphs with a Small Smallest Eigenvalue
نویسندگان
چکیده
منابع مشابه
On distance-regular graphs with smallest eigenvalue at least -m
A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m ≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least −m, diameter at least three and intersection number c2 ≥ 2.
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Godsil showed that if Γ is a distance-regular graph with diameter D > 3 and valency k > 3, and θ is an eigenvalue of Γ with multiplicity m > 2, then k 6 (m+2)(m−1) 2 . In this paper we will give a refined statement of this result. We show that if Γ is a distance-regular graph with diameter D > 3, valency k > 2 and an eigenvalue θ with multiplicity m > 2, such that k is close to (m+2)(m−1) 2 , t...
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In this paper, all connected bipartite graphs are characterized whose third largest Laplacian eigenvalue is less than three. Moreover, the result is used to characterize all connected bipartite graphs with exactly two Laplacian eigenvalues not less than three, and all connected line graphs of bipartite graphs with the third eigenvalue of their adjacency matrices less than one. c © 2003 Elsevier...
متن کاملDistance-regular graphs with an eigenvalue
It is known that bipartite distance-regular graphs with diameter D > 3, valency k > 3, intersection number c2 > 2 and eigenvalues k = θ0 > θ1 > · · · > θD satisfy θ1 6 k− 2 and thus θD−1 > 2− k. In this paper we classify non-complete distanceregular graphs with valency k > 2, intersection number c2 > 2 and an eigenvalue θ satisfying −k < θ 6 2 − k. Moreover, we give a lower bound for valency k ...
متن کاملA characterization of bipartite distance-regular graphs
Article history: Received 9 April 2013 Accepted 15 December 2013 Available online 13 January 2014 Submitted by R. Brualdi
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8361