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

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 d...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Lubna Gul, Gohar Ali, Usama Waheed, Nudrat Aamir
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/acca7c0a1b7b47e7b927ec7529ec8b2b
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:acca7c0a1b7b47e7b927ec7529ec8b2b
record_format	dspace
spelling	oai:doaj.org-article:acca7c0a1b7b47e7b927ec7529ec8b2b2021-11-29T00:55:38ZThe Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix2314-478510.1155/2021/8016237https://doaj.org/article/acca7c0a1b7b47e7b927ec7529ec8b2b2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8016237https://doaj.org/toc/2314-4785All 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.Lubna GulGohar AliUsama WaheedNudrat AamirHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Lubna Gul Gohar Ali Usama Waheed Nudrat Aamir The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
description	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.
format	article
author	Lubna Gul Gohar Ali Usama Waheed Nudrat Aamir
author_facet	Lubna Gul Gohar Ali Usama Waheed Nudrat Aamir
author_sort	Lubna Gul
title	The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
title_short	The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
title_full	The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
title_fullStr	The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
title_full_unstemmed	The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
title_sort	optimal graph whose least eigenvalue is minimal among all graphs via 1-2 adjacency matrix
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/acca7c0a1b7b47e7b927ec7529ec8b2b
work_keys_str_mv	AT lubnagul theoptimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT goharali theoptimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT usamawaheed theoptimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT nudrataamir theoptimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT lubnagul optimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT goharali optimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT usamawaheed optimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix AT nudrataamir optimalgraphwhoseleasteigenvalueisminimalamongallgraphsvia12adjacencymatrix
_version_	1718407790634991616

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

Ejemplares similares