Distance-regular Cayley graphs with least eigenvalue $$-2$$ - 2
نویسندگان
چکیده
منابع مشابه
Distance-regular Cayley graphs with least eigenvalue -2
We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular C...
متن کاملOn 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.
متن کاملNotes on graphs with least eigenvalue at least -2
A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. E...
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 کاملDistance-regular Cayley graphs on dihedral groups
The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every nontrivial distance-regular Cayley graph on a dihedral group...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2016
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-016-0209-4