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

Document Type : Research Paper


1 Department of Mathematics‎, ‎Science and Research Branch‎, ‎Islamic Azad University‎, ‎Tehran‎, ‎Iran

2 Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan 87317-51167‎, ‎Iran


‎Let $ \sum_{i=0}^{n}(-1)^il_ix^{n-i}$ and $\sum_{i=0}^{n}(-1)^iq_ix^{n-i}$ be the characteristic polynomials of the Laplacian matrix and signless Laplacian matrix of an $n$-vertex graph‎, ‎respectively‎. ‎Let $\alpha_i = |q_i‎ - ‎l_i|$‎, ‎$0\leq i \leq n$‎. ‎In this paper‎, ‎we find formulas for some of $\alpha_i$'s‎. ‎In particular‎, ‎we compute $\alpha_i$'s for some fullerene graphs.


Main Subjects

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Volume 15, Issue 1
Special Issue Dedicated to the memory of Professor Ali Reza Ashrafi (University of Kashan, I.R. Iran), who was the creator and the Editor-in-Chief of IJMC for 14 years.
March 2024
Pages 39-50