Abstract
The total graph of a ring R, denoted as T(Ī(R)), is defined to be a graph with vertex set V(T(Ī(R)))=R and two distinct vertices u,vāV(T(Ī(R))) are adjacent if and only if u+vāZ(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(GĆH)=V(G)ĆV(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_2āH; or 2) v_1=v_2 and u_1 u_2āE(G). An isomorphism of graphs G dan H is a bijection Ļ:V(G)āV(H) such that u,vāV(G) are adjacent if and only if f(u),f(v)āV(H) are adjacent. This paper proved that T(Ī(Z_2p )) and P_2ĆK_p are isomorphic for every odd prime p.
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