Some Inequalities for the First General Zagreb Index of Graphs and Line Graphs
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, cilt.91, sa.1, ss.79-88, 2021 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 91 Sayı: 1
- Basım Tarihi: 2021
- Doi Numarası: 10.1007/s40010-020-00679-9
- Dergi Adı: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
- Sayfa Sayıları: ss.79-88
- Anahtar Kelimeler: First Zagreb index, General first Zagreb index, Line graph, Jump graph, Iterated line graph
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
The first general Zagreb index M1 alpha(G) of a graph G is equal to the sum of the alpha th powers of the vertex degrees of G. For alpha >= 0 and k >= 1, we obtain the lower and upper bounds for M1 alpha(G) and M1 alpha(L(G)) in terms of order, size, minimum/maximum vertex degrees and minimal non-pendant vertex degree using some classical inequalities and majorization technique, where L(G) is the line graph of G. Also, we obtain some bounds and exact values of M1 alpha(J(G)) and M1 alpha(Lk(G)), where J(G) is a jump graph (complement of a line graph) and Lk(G) is an iterated line graph of a graph G.