TY - JOUR

T1 - CONNECTIVITY INDICES OF COPRIME GRAPH OF GENERALIZED QUATERNION GROUP

AU - Zahidah, Siti

AU - Mahanani, Dwi Mifta

AU - Oktaviana, Karine Lutfiah

N1 - Publisher Copyright:
© 2021 The Indonesian Mathematical Society. All Rights Reserved.

PY - 2021/12/2

Y1 - 2021/12/2

N2 - Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x2n = y4 = e and xy = yx−1. The coprime graph of Q4n, denoted by ΩQ4n, is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.

AB - Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x2n = y4 = e and xy = yx−1. The coprime graph of Q4n, denoted by ΩQ4n, is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.

KW - Generalized quaternion group

KW - Harary index

KW - Szeged index

KW - Wiener indices

KW - Zagreb indices

UR - http://www.scopus.com/inward/record.url?scp=85124949940&partnerID=8YFLogxK

U2 - 10.22342/jims.27.3.1043.285-296

DO - 10.22342/jims.27.3.1043.285-296

M3 - Article

AN - SCOPUS:85124949940

SN - 2086-8952

VL - 27

SP - 285

EP - 296

JO - Journal of the Indonesian Mathematical Society

JF - Journal of the Indonesian Mathematical Society

IS - 3

ER -