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The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix

Author

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  • Lubna Gul
  • Gohar Ali
  • Usama Waheed
  • Nudrat Aamir
  • Elena Guardo

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.

Suggested Citation

  • Lubna Gul & Gohar Ali & Usama Waheed & Nudrat Aamir & Elena Guardo, 2021. "The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix," Journal of Mathematics, Hindawi, vol. 2021, pages 1-4, November.
    • Handle: RePEc:hin:jjmath:8016237
    DOI: 10.1155/2021/8016237
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