On the relation of the total graph of a ring and a product of graphs

Jauhari, Mohammad Nafie (2022) On the relation of the total graph of a ring and a product of graphs. Jurnal Matematika : MANTIK, 8 (2). pp. 99-104. ISSN 2527-3167

Preview

Text 13523.pdf - Published Version Available under License Creative Commons Attribution Non-commercial Share Alike. Download (490kB) | Preview

Abstract

The total graph of a ring R, denoted as T(Γ(R)), is defined to be a graph with vertex set V(T(Γ(R)))=R and two distinct vertices u,v∈V(T(Γ(R))) are adjacent if and only if u+v∈Z(R), where Z(R) is the zero divisor of R. The Cartesian product of two graphs G and H is a graph with the vertex set V(G×H)=V(G)×V(H) and two distinct vertices (u_1,v_1 ) and (u_2,v_2 ) are adjacent if and only if: 1) u_1=u_2 and v_1 v_2∈H; or 2) v_1=v_2 and u_1 u_2∈E(G). An isomorphism of graphs G dan H is a bijection ϕ:V(G)→V(H) such that u,v∈V(G) are adjacent if and only if f(u),f(v)∈V(H) are adjacent. This paper proved that T(Γ(Z_2p )) and P_2×K_p are isomorphic for every odd prime p.

Item Type:	Journal Article
Keywords:	group; total graph; isomorphism; cartesian product
Subjects:	01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Mohammad Nafie Jauhari
Date Deposited:	27 Apr 2023 13:30

Downloads

Origin of downloads

Actions (login required)

View Item