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 -