No two Jellyfish graphs are L-cospectral and Q-cospectral
In this paper, it is proved that the jellyfish graphs, a natural generalization of sun graphs, are both DLS and DQS.
math.CO↗
arXiv subjects
A. Z. Abdian
Publications and source records attributed to A. Z. Abdian.
Laplacian Spectral Determination of Path-Friendship Graphs
A graph $G$ is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to $G$. van Dam and Haemers (2003) conjectured that almost all graphs have this property, but that is known to be the case only for a very few families. In some recent papers it is proved that the friendship graphs and starlike trees are DLS. If a friendship graph and a starlike tree are joined by merging their vertices of degree greater than 2, then the resulting graph is called a path-friendship graph. In this paper, it is proved that the path-friendship graphs are also DLS.
math.CO↗
Signless Laplacian determinations of some graphs with independent edges
{Signless Laplacian determinations of some graphs with independent edges}% {Let $G$ be a simple undirected graph. Then the signless Laplacian matrix of $G$ is defined as $D_G + A_G$ in which $D_G$ and $A_G$ denote the degree matrix and the adjacency matrix of $G$, respectively. The graph $G$ is said to be determined by its signless Laplacian spectrum ({\rm DQS}, for short), if any graph having the same signless Laplacian spectrum as $G$ is isomorphic to $G$. We show that $G\sqcup rK_2$ is determined by its signless Laplacian spectra under certain conditions, where $r$ and $K_2$ denote a natural number and the complete graph on two vertices, respectively. Applying these results, some {\rm DQS} graphs with independent edges are obtained.
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