Speaker
Jitul Talukdar
(IIT Kharagpur)
Description
Abstract: In this paper, we investigate when the disjoint union of complete graphs $K_a \cup K_b$ is determined by its signless Laplacian spectrum (Q-DS). We first prove that $K_a \cup K_b$ is Q-DS among disconnected graphs. We then show that no connected signless Laplacian co-spectral mate of $K_a \cup K_b$ exists on at most ten vertices. Further, we establish that $K_t \cup K_a$ is Q-DS for $t=1,2$, except in the case $t=1$ and $a=3$. We also prove that $K_a \cup K_{a+1}$ is Q-DS. Finally, we show that the complete bipartite graph $K_{a,a+1}$ is determined by its signless Laplacian spectrum.
Keywords: Complete graph; Co-spectral graph; Signless Laplacian
matrix.
AMS subject classifications: 05C50, 15A18.
Author
Jitul Talukdar
(IIT Kharagpur)