On the Difference between Laplacian and Signless Laplacian Coefficients of a Graph and its Applications on the Fullerene Graphs

Abstract

L e t sigma_{i=0}^n (-1)^il_ix^(n-i) and sigma_{i=0}^n (-1)^iq_ix^(n-i) b e t h e c h a r - a c t e r i s t i c p o l y n o m i a l s o f t h e L a p l a c i a n m a t r i x a n d s i g n l e s s L a p l a c i a n m a t r i x o f a n n- v e r t e x g r a p h , r e s p e c t i v e l y . L e t alpha_i=|q_i-l_i|. I n t h i s p a p e r , w e fi n d f o r m u l a s f o r s o m e o f αi’ s . I n p a r t i c u l a r , w e c o mp u t e αi’ s f o r s o me f u l l e r e n e g r a p h s .