TY - JOUR
T1 - Characterizing Graphs with Nullity n−4
AU - Poojary, Raksha
AU - Bhat, Arathi K.
AU - Karantha, Manjunatha Prasad
AU - Arumugam, S.
AU - Gutman, Ivan
N1 - Funding Information:
Acknowledgment: Author Manjunatha Prasad Karantha acknowledge the support by Science and Engineering Research Board (DST), India through the projects CRG/2019/000238 and MTR/2018/000156
Publisher Copyright:
© 2023 University of Kragujevac, Faculty of Science. All rights reserved.
PY - 2023
Y1 - 2023
N2 - The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n − 4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n − 4 are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity n − 4.
AB - The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n − 4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n − 4 are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity n − 4.
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U2 - 10.46793/match.89-3.631P
DO - 10.46793/match.89-3.631P
M3 - Article
AN - SCOPUS:85150162209
SN - 0340-6253
VL - 89
SP - 631
EP - 642
JO - Match
JF - Match
IS - 3
ER -