Akademik Veri Yönetim Sistemi
Palestine Journal of Mathematics, cilt.14, sa.Special issue 3, ss.81-90, 2025 (Scopus)
We study a class of bipartite graphs, termed bipartite Kneser B-type-k graphs, denoted by HB (n, k). Let Bn = {±a1, ±a2, …, ±an−1, an} be a set where n > 1 is a fixed integer, and each ai ∈ R+ such that a1 < a2 < · · · < an. Define ϕ(Bn) as the collection of all non-empty subsets S = {x1, x2, …, xt} of Bn satisfying the ordering condition |x1 | < |x2 | < · · · < |xt−1 | < xt, where xt ∈ R+. Let B+n = {a1, a2, …, an} be the strictly positive elements of Bn. The vertex set of HB (n, k) consists of two partitions: V1, the collection of all k-element subsets of B+n, where 1 ≤ k < n, and V2, defined as V2 = ϕ(Bn) − V1 . For any X ∈ V2, its transformed set is given by X† = {|x|: x ∈ X}. Edges exist between a vertex A ∈ V1 and B ∈ V2 if and only if A ⊂ B† or B† ⊂ A. We analyze fundamental graph invariants of HB (n, k), including its degree sequence. Our results provide insights into the combinatorial nature of this special class of bipartite graphs.