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On Trees with Given Independence Numbers with Maximum Gourava Indices
- Source :
- Symmetry, Vol 15, Iss 2, p 308 (2023)
- Publication Year :
- 2023
- Publisher :
- MDPI AG, 2023.
-
Abstract
- In mathematical chemistry, molecular descriptors serve an important role, primarily in quantitative structure–property relationship (QSPR) and quantitative structure–activity relationship (QSAR) studies. A topological index of a molecular graph is a real number that is invariant under graph isomorphism conditions and provides information about its size, symmetry, degree of branching, and cyclicity. For any graph N, the first and second Gourava indices are defined as GO1(N)=∑u′v′∈E(N)(d(u′)+d(v′)+d(u′)d(v′)) and GO2(N)=∑u′v′∈E(N)(d(u′)+d(v′))d(u′)d(v′), respectively.The independence number of a graph N, being the cardinality of its maximal independent set, plays a vital role in reading the energies of chemical trees. In this research paper, it is shown that among the family of trees of order δ and independence number ξ, the spur tree denoted as Υδ,ξ maximizes both 1st and 2nd Gourava indices, and with these characterizations this graph is unique.
- Subjects :
- tree
spur tree
independence number
Gourava indices
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 15
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Symmetry
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.62a82a8939cb4568bb091229a1971e66
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/sym15020308