NDLI: Mathematical Properties of Variable Topological Indices

Please wait, while we are loading the content...

Mathematical Properties of Variable Topological Indices

Content Provider	MDPI
Author	Sigarreta, José M.
Copyright Year	2020
Abstract	A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices $A_{α}$ and $B_{α}$ , defined for each graph $H = (V (H), E (H))$ by $A_{α} (H) = \sum_{i j \in E (H)} f {(d_{i}, d_{j})}^{α}$ and $B_{α} (H) = \sum_{i \in V (H)} h {(d_{i})}^{α}$ , where $d_{i}$ denotes the degree of the vertex i and $α$ is any real number. Many important topological indices can be obtained from $A_{α}$ and $B_{α}$ by choosing appropriate symmetric functions and values of $α$ . This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of $A_{α}$ (respectively, $B_{α}$ ) involving $A_{β}$ (respectively, $B_{β}$ ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.
Starting Page	43
e-ISSN	20738994
DOI	10.3390/sym13010043
Journal	Symmetry
Issue Number	1
Volume Number	13
Language	English
Publisher	MDPI
Publisher Date	2020-12-30
Access Restriction	Open
Subject Keyword	Symmetry Logic Variable Zagreb Indices Variable Sum-connectivity Index Variable Geometric-arithmetic Index Variable Inverse Sum Indeg Index
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in