Geodesic
Signless Laplacian spectral determination of path-friendship graphs
Reza Sharafdini1 ; Ali Zeydi Abdian2 ; Reza Sharafdini ; Ali Zeydi Abdian
1Department of Mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran
2Department of Mathematical Sciences, Lorestan University, College of Science, Lorestan, Khoramabad, Iran
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 3, pp. 245-258 
Reza Sharafdini; Ali Zeydi Abdian; Reza Sharafdini; Ali Zeydi Abdian. Signless Laplacian spectral determination of path-friendship graphs. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 3, pp. 245-258. http://geodesic.mathdoc.fr/item/AMUC_2021_90_3_a0/
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     title = { Signless {Laplacian} spectral determination of path-friendship graphs},
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A graph $G$ is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum as $G$. Let $k$, $t_i$ ($1\leq i\leq k$), and $s$ be natural numbers. A path-friendship graph, $G_{s, t_1, \dots, t_k}$, is a graph of order $n=2s+t_1+\cdots+t_k+1$ which consists of $s$ triangles and $k$ paths of lengths $t_1, t_2,\ldots, t_k $ sharing a common vertex. In this paper, we show that these graphs are DQS and using this result, we respond to a conjecture in [F. Wen, Q. Huang, X. Huang and F. Liu, The spectral characterization of wind-wheel graphs, Indian J. Pure Appl. Math. 46 (2015), 613--631].