Ad-Hoc Lanzhou Index

Akbar Ali, Yilun Shang, Darko Dimitrov () and Tamás Réti
Additional contact information
Akbar Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
Darko Dimitrov: Faculty of Information Studies, 8000 Novo Mesto, Slovenia
Tamás Réti: Donát Bánki Faculty of Mechanical and Safety Engineering, Óbuda University, H-1034 Budapest, Hungary

Mathematics, 2023, vol. 11, issue 20, 1-19

Abstract: This paper initiates the study of the mathematical aspects of the ad-hoc Lanzhou index. If G is a graph with the vertex set { x 1 , … , x n } , then the ad-hoc Lanzhou index of G is defined by L z ˜ ( G ) = ∑ i = 1 n d i ( n − 1 − d i ) 2 , where d i represents the degree of the vertex x i . Several identities for the ad-hoc Lanzhou index, involving some existing topological indices, are established. The problems of finding graphs with the extremum values of the ad-hoc Lanzhou index from the following sets of graphs are also attacked: (i) the set of all connected ξ -cyclic graphs of a fixed order, (ii) the set of all connected molecular ξ -cyclic graphs of a fixed order, (iii) the set of all graphs of a fixed order, and (iv) the set of all connected molecular graphs of a fixed order.

Keywords: topological index; chemical graph theory; ad-hoc Lanzhou index; Lanzhou index; forgotten topological coindex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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