Study of Prime Graph of a Ring

Kishor Pawar, Sandeep Joshi

Abstract


The notion of a prime graph of a ring $R$, ($PG(R)$) was first introduced by {\sc S. Bhavanari and his coauthors} in [1]. In this paper, we introduce the notion of `Complement of a Prime Graph of a Ring $R$', denote it by $(PG(R))^c$ and find the degree of vertices in $PG(R)$ and $(PG(R))^c$ for the ring $\mz_n$ and the number of triangles in $PG(R)$ and $(PG(R))^c$. It is proved that for any $n \geq 6$ which not a prime then $gr(PG(\mz_n ))=3$. If $n$ is any prime number or $n=4$ then $gr(PG(\mz_n))= \infty$.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|