On the second minimizing graph in the set of complements of trees

On the second minimizing graph in the set of complements of trees

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Let G be a graph of order n and A(G)=[ai,j]be its adjacency matrix such that ai,j=1 if viis adjacent to vjand ai,j=0 otherwise, where 1≤i,j≤n. In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of its adjacency matrix attains the minimum (or se...

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Main Author: M. Javaid
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860016301554
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spelling doaj-37fb43a770324d5c9457bf124b5b84ee2020-11-25T03:21:40ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163258264On the second minimizing graph in the set of complements of treesM. Javaid0Department of Mathematics, School of Science, University of Management and Technology (UMT), Lahore, PakistanLet G be a graph of order n and A(G)=[ai,j]be its adjacency matrix such that ai,j=1 if viis adjacent to vjand ai,j=0 otherwise, where 1≤i,j≤n. In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of its adjacency matrix attains the minimum (or second minimum). In this paper, we characterize the second minimizing graph among all graphs which belong to the set of complements of the trees. Keywords: Adjacency matrix, Least eigenvalue, Complement of treeshttp://www.sciencedirect.com/science/article/pii/S0972860016301554
collection DOAJ
language English
format Article
sources DOAJ
author M. Javaid
spellingShingle M. Javaid
On the second minimizing graph in the set of complements of trees
AKCE International Journal of Graphs and Combinatorics
author_facet M. Javaid
author_sort M. Javaid
title On the second minimizing graph in the set of complements of trees
title_short On the second minimizing graph in the set of complements of trees
title_full On the second minimizing graph in the set of complements of trees
title_fullStr On the second minimizing graph in the set of complements of trees
title_full_unstemmed On the second minimizing graph in the set of complements of trees
title_sort on the second minimizing graph in the set of complements of trees
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
publishDate 2019-12-01
description Let G be a graph of order n and A(G)=[ai,j]be its adjacency matrix such that ai,j=1 if viis adjacent to vjand ai,j=0 otherwise, where 1≤i,j≤n. In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of its adjacency matrix attains the minimum (or second minimum). In this paper, we characterize the second minimizing graph among all graphs which belong to the set of complements of the trees. Keywords: Adjacency matrix, Least eigenvalue, Complement of trees
url http://www.sciencedirect.com/science/article/pii/S0972860016301554
work_keys_str_mv AT mjavaid onthesecondminimizinggraphinthesetofcomplementsoftrees
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