AbstractWe study the graphs D(k,q) of [4] with particular emphasis on their connected components when q is odd. In [6] the authors proved that these components (most often) provide the best-known asymptotic lower bound for the greatest number of edges in graphs of their order and girth. It was further shown in [6] that D(k,q) has at least qt−1 components, where t = ⌊(k + 2)/4⌋. In this paper we prove that the value qt−1 is precise and that the numerical invariant introduced in [6] completely characterizes the components of D(k,q). Some general results regarding the relationship between D(l,q) and D(k,q) (l < k) are also obtained
AbstractLet Γ be an antipodal distance-regular graph with diameter 4 and eigenvalues θ0>θ1>θ2>θ3>θ4....
AbstractLet f(r) denote the smallest number of points in a non-bipartite r-regular graph of girth 4....
AbstractLet ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined a...
AbstractWe study the graphs D(k,q) of [4] with particular emphasis on their connected components whe...
AbstractLet q be a prime power and k⩾2 be an integer. Lazebnik et al. (Rutcor Research Report RRR 99...
AbstractLet q be a prime power and k⩾2 be an integer. Lazebnik et al. (Rutcor Research Report RRR 99...
Several upper bounds are given for the maximum number of edges e possible in a graph depending upon ...
Several upper bounds are given for the maximum number of edges e possible in a graph depending upon ...
Let k ≥ 1 be an odd integer, t = ⌊ k+2 ⌋, and q be a prime power. We 4 construct a bipartite, q–reg...
AbstractThe odd girth of a graph G gives the length of a shortest odd cycle in G. Let ƒ(k, g) denote...
A subdivision of K4 is called an odd-K4 if each triangle of the K4 is subdivided to form an odd cycl...
Abstract. We will examine the maximal number of edges of a graph on p vertices of order dimension 4....
AbstractThe odd girth of a graph G gives the length of a shortest odd cycle in G. Let ƒ(k, g) denote...
AbstractLet R(Cn, Cp) be the smallest integer m for which the following statement is true: If a G gr...
Let V denote a d-dimensional vector space over Fq. Associated to V is a distance-regular graph Quad(...
AbstractLet Γ be an antipodal distance-regular graph with diameter 4 and eigenvalues θ0>θ1>θ2>θ3>θ4....
AbstractLet f(r) denote the smallest number of points in a non-bipartite r-regular graph of girth 4....
AbstractLet ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined a...
AbstractWe study the graphs D(k,q) of [4] with particular emphasis on their connected components whe...
AbstractLet q be a prime power and k⩾2 be an integer. Lazebnik et al. (Rutcor Research Report RRR 99...
AbstractLet q be a prime power and k⩾2 be an integer. Lazebnik et al. (Rutcor Research Report RRR 99...
Several upper bounds are given for the maximum number of edges e possible in a graph depending upon ...
Several upper bounds are given for the maximum number of edges e possible in a graph depending upon ...
Let k ≥ 1 be an odd integer, t = ⌊ k+2 ⌋, and q be a prime power. We 4 construct a bipartite, q–reg...
AbstractThe odd girth of a graph G gives the length of a shortest odd cycle in G. Let ƒ(k, g) denote...
A subdivision of K4 is called an odd-K4 if each triangle of the K4 is subdivided to form an odd cycl...
Abstract. We will examine the maximal number of edges of a graph on p vertices of order dimension 4....
AbstractThe odd girth of a graph G gives the length of a shortest odd cycle in G. Let ƒ(k, g) denote...
AbstractLet R(Cn, Cp) be the smallest integer m for which the following statement is true: If a G gr...
Let V denote a d-dimensional vector space over Fq. Associated to V is a distance-regular graph Quad(...
AbstractLet Γ be an antipodal distance-regular graph with diameter 4 and eigenvalues θ0>θ1>θ2>θ3>θ4....
AbstractLet f(r) denote the smallest number of points in a non-bipartite r-regular graph of girth 4....
AbstractLet ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined a...