TY - JOUR
T1 - Some graphs determined by their (signless) Laplacian spectra
AU - Liu, Muhuo
AU - Shan, Haiying
AU - Das, Kinkar Ch
PY - 2014/5/15
Y1 - 2014/5/15
N2 - A graph G is L-DS (respectively, Q-DS) if there is no other non-isomorphic graph with the same (respectively, signless) Laplacian spectrum as G. Let G1â̂̈G2 be the join graph of graphs G1 and G2, and Ur,n-r the graph obtained by attaching n-r pendent vertices to a vertex of Cr (the cycle of order r). In this paper, we prove that if G is L-DS and the algebraic connectivity of G is less than three, then Ktâ̂̈G is L-DS under certain condition, which extends the main result of Zhou and Bu (2012) [24]. Also, Ur,n-r is proved to be Q-DS for r≥3.
AB - A graph G is L-DS (respectively, Q-DS) if there is no other non-isomorphic graph with the same (respectively, signless) Laplacian spectrum as G. Let G1â̂̈G2 be the join graph of graphs G1 and G2, and Ur,n-r the graph obtained by attaching n-r pendent vertices to a vertex of Cr (the cycle of order r). In this paper, we prove that if G is L-DS and the algebraic connectivity of G is less than three, then Ktâ̂̈G is L-DS under certain condition, which extends the main result of Zhou and Bu (2012) [24]. Also, Ur,n-r is proved to be Q-DS for r≥3.
KW - Algebraic connectivity
KW - Join graph
KW - Laplacian spectrum
KW - Signless Laplacian spectrum
UR - https://www.scopus.com/pages/publications/84896760029
U2 - 10.1016/j.laa.2014.02.027
DO - 10.1016/j.laa.2014.02.027
M3 - Article
AN - SCOPUS:84896760029
SN - 0024-3795
VL - 449
SP - 154
EP - 165
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -