ON COMMUTING GRAPHS OF GROUP RING Z_{n}Q_{8}

- Journal title : Communications of the Korean Mathematical Society
- Volume 27, Issue 1, 2012, pp.57-68
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2012.27.1.057

Title & Authors

ON COMMUTING GRAPHS OF GROUP RING Z_{n}Q_{8}

Chen, Jianlong; Gao, Yanyan; Tang, Gaohua;

Chen, Jianlong; Gao, Yanyan; Tang, Gaohua;

Abstract

The commuting graph of an arbitrary ring R, denoted by , is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of group ring . The main result is that is connected if and only if n is not a prime. If is connected, then diam()= 3, while is disconnected then every connected component of must be a complete graph with a same size. Further, we obtain the degree of every vertex in , the maximum degree and the minimum degree of .

Keywords

group ring;commuting graph;connected component;diameter of a graph;

Language

English

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