University of KashanMathematics Interdisciplinary Research2538-36394220191201The Fourth and Fifth Laplacian Coefficients of some Rooted Trees18319210158810.22052/mir.2020.207378.1173ENMahsaArabzadehDepartment of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. IranGholam-HosseinFath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan,
Kashan, I. R. IranHamidRasoliDepartment of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. IranAbolfazlTehranianDepartment of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. IranJournal Article20191103Abstract. The Laplacian characteristic polynomial of an n-vertex graph G has the form f(G,x) = x<sup>n</sup>+∑l<sub>ix</sub><sup>n</sup>-i. In this paper, the fourth and fifth coefficient of f(G,x), will be investigated, where G is a T(k,t) tree in which a rooted tree with degree sequence k,k,...,k,1,1,...,1 is denoted by T(k,t).https://mir.kashanu.ac.ir/article_101588_f54ef31c99328589cc826b00c2bd8846.pdf