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The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
- Source :
- Journal of Mathematics, Vol 2021 (2021)
- Publication Year :
- 2021
- Publisher :
- Wiley, 2021.
-
Abstract
- All graphs under consideration are finite, simple, connected, and undirected. Adjacency matrix of a graph G is 0,1 matrix A=aij=0, if vi=vj or dvi,vj≥21, if dvi,vj=1.. Here in this paper, we discussed new type of adjacency matrix known by 1-2 adjacency matrix defined as A1,2G=aij=0, if vi=vj or dvi,vj≥31, if dvi,vj=2, from eigenvalues of the graph, we mean eigenvalues of the 1-2 adjacency matrix. Let Tnc be the set of the complement of trees of order n. In this paper, we characterized a unique graph whose least eigenvalue is minimal among all the graphs in Tnc.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 23144785
- Volume :
- 2021
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.7c0a1b7b47e7b927ec7529ec8b2b
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2021/8016237