On strongly regular graphs with m2 = qm3 and m3 = qm2 where q ∈ Q
نویسندگان
چکیده
We say that a regular graph G of order n and degree r ? 1 (which is not the complete graph) strongly if there exist non-negative integers such |Si Sj | = for any two adjacent vertices i j, distinct non-adjacent where Sk denotes neighborhood vertex k. Let ?1 r, ?2 ?3 be eigenvalues connected graph. m1 1, m2 m3 denote multiplicity ?3, respectively. here describe parameters n, graphs with qm3 qm2 q 3/2, 4/3, 5/2, 5/3, 5/4, 6/5.
منابع مشابه
q - regular bipartite graphs
An explicit construction of a family of binary LDPC codes called LU(3, q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.
متن کاملTRANSITIVE t - DESIGNS AND STRONGLY REGULAR GRAPHS CONSTRUCTED FROM LINEAR GROUPS L ( 2 , q ) , q ≤ 23
In this paper we construct transitive t-designs from the linear groups L(2, q), q ≤ 23. Thereby we classify t-designs, t ≥ 2, admitting a transitive action of the linear groups L(2, q), q ≤ 23, up to 35 points and obtained numerous transitive designs, for 36 ≤ v ≤ 55. In many cases we proved the existence of t-designs with certain parameter sets. Among others we constructed t-designs with param...
متن کاملOn bipartite Q-polynomial distance-regular graphs
Let Γ denote a bipartite Q-polynomial distance-regular graph with vertex set X, diameter d ≥ 3 and valency k ≥ 3. Let RX denote the vector space over R consisting of column vectors with entries in R and rows indexed by X. For z ∈ X, let ẑ denote the vector in RX with a 1 in the z-coordinate, and 0 in all other coordinates. Fix x, y ∈ X such that ∂(x, y) = 2, where ∂ denotes path-length distance...
متن کاملOn regular (1, q)-extendable graphs
Let G be a graph with a maximum matching of size q, and let p ≤ q be a positive integer. Then G is called (p, q)-extendable if every set of p independent edges can be extended to a matching of size q. If G is a graph of even order n and 2q = n, then (p, q)-extendable graphs are exactly the p-extendable graphs defined by Plummer [Discrete Math. 31 (1980), 201–210]. Let d ≥ 3 be an integer, and l...
متن کاملAlmost-bipartite distance-regular graphs with the Q-polynomial property
Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD 6= 0. We show that Γ is a polygon, a folded cube, or an Odd graph.
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: Publications De L'institut Mathematique
سال: 2021
ISSN: ['0350-1302', '1820-7405']
DOI: https://doi.org/10.2298/pim2123035l