Spectrum of bipartite Kneser type-k graphs
Palestine Journal of Mathematics, cilt.14, sa.Special Issue 3, ss.51-61, 2025 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: Special Issue 3
- Basım Tarihi: 2025
- Dergi Adı: Palestine Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.51-61
- Anahtar Kelimeler: bipartite Kneser graphs, bipartite Kneser type-k graphs, chemical graphs, Set inclusion graphs, spectrum
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
Let n and k be integers with n > 1, k ≥ 1. Let [n] = {1, 2, 3, …, n}. Let ϕ([n]) be the set of all non-empty subsets of [n]. Let V1 be the set of all k-element subsets of [n] and V2 = ϕ([n])−V1. A bipartite Kneser type-k graph HT (n, k) is a graph with vertex set V = V1∪V2 in which a vertex of V1 is adjacent to a vertex of V2 if and only if the set corresponding to one of the vertices is a subset of the set corresponding to the other vertex. The spectrum becomes an important molecular structure descriptor when thinking of chemical graphs. In this paper, we determined the spectrum of HT (n, k) and some of its characteristics. We also analysed the spectrum of the line graph of HT (n, k). It has been observed that the least eigenvalue of the line graph of HT (n, k) is −2.