Article
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Ad-Hoc Lanzhou Index
Version 1
: Received: 26 September 2023 / Approved: 26 September 2023 / Online: 28 September 2023 (09:53:05 CEST)
A peer-reviewed article of this Preprint also exists.
Ali, A.; Shang, Y.; Dimitrov, D.; Réti, T. Ad-Hoc Lanzhou Index. Mathematics 2023, 11, 4256. Ali, A.; Shang, Y.; Dimitrov, D.; Réti, T. Ad-Hoc Lanzhou Index. Mathematics 2023, 11, 4256.
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 {x1,⋯,xn}, then the ad-hoc Lanzhou index of G is defined by Lz¯(G)=∑i=1ndi(n−1−di)2, where di represents the degree of the vertex xi. 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) set of all connected ξ-cyclic graphs of a fixed order, (ii) set of all connected molecular ξ-cyclic graphs of a fixed order, (iii) set of all graphs of a fixed order, (iv) 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
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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