UGC Approved Journal no 63975(19)
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ISSN: 2349-5162 | ESTD Year : 2014
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Published in:

Volume 6 Issue 6
June-2019
eISSN: 2349-5162

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Published Paper ID:
JETIR1906513


Registration ID:
213849

Page Number

508-518

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Title

A COMPREHENSIVE REVIEW ON ADJACENCY MATRICES OF GRAPHS WITH A GIVEN RANK AND LAPLACIAN OPERATOR

Abstract

We took for the following results. Two graphs G_1 and G_2 are isomorphic if and only if their incidence matrices A(G_1 ) and A(G_2 ) differ only by permutation of rows and columns, If A(G) is an incidence matrix of a connected graph G with n vertices, then rank of A(G) is n-1, The reduced incidence matrix of a tree is non-singular, The Laplacian L_G is singular and positive semi definite and χ(G)≥1+λ_min⁡ /λ_max⁡ .

Key Words

Graphs, Trees, Adjacency Matrix & Incidence Matrix & Rank of a Matrix.

Cite This Article

"A COMPREHENSIVE REVIEW ON ADJACENCY MATRICES OF GRAPHS WITH A GIVEN RANK AND LAPLACIAN OPERATOR", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 6, page no.508-518, June-2019, Available :http://www.jetir.org/papers/JETIR1906513.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"A COMPREHENSIVE REVIEW ON ADJACENCY MATRICES OF GRAPHS WITH A GIVEN RANK AND LAPLACIAN OPERATOR", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 6, page no. pp508-518, June-2019, Available at : http://www.jetir.org/papers/JETIR1906513.pdf

Publication Details

Published Paper ID: JETIR1906513
Registration ID: 213849
Published In: Volume 6 | Issue 6 | Year June-2019
DOI (Digital Object Identifier):
Page No: 508-518
Country: Kalippatti, Namakkal, Tamilnadu, India .
Area: Mathematics
ISSN Number: 2349-5162
Publisher: IJ Publication
Published Paper URL :: https://www.jetir.org/view?paper=JETIR1906513
Published Paper PDF: https://www.jetir.org/papers/JETIR1906513

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