A Further Note on the Graph of Monogenic Semigroups

Authors : Nihat AKGÜNEŞ

Pages : 49-53

View : 19 | Download : 13

Publication Date : 2018-04-15

Article Type : Research Paper

Abstract :In [15], it has been recently defined a new graph $\Gamma insert ignore into journalissuearticles values({% \mathcal{S}}_{M});$ on monogenic semigroups ${\mathcal{S}}_{M}$ insert ignore into journalissuearticles values(with zero); having elements $\{0,x,x^{2},x^{3},\cdots ,x^{n}\}$. The vertices are the non-zero elements $x,x^{2},x^{3},\cdots ,x^{n}$ and, for $1\leq i,j\leq n$, any two distinct vertices $x^{i}$ and $x^{j}$ are adjacent if $x^{i}x^{j}=0$ in ${\mathcal{S}}_{M}$. As a continuing study of [3] and [15], in this paper it will be investigated some special parameters insert ignore into journalissuearticles values(such as covering number, accessible number, independence number);, first and second multiplicative Zagreb indices, and Narumi-Katayama index. Furthermore, it will be presented Laplacian eigenvalue and Laplacian characteristic polynomial for $\Gamma insert ignore into journalissuearticles values({\mathcal{S}}_{M});$.
Keywords : Laplacian Polynomial, Narumi Katayama Index, Monogenic Semigroups, Graph, Laplacian Eigenvalue, Narumi Katayama Index