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MULTIPLE CO-PRIME DIVISORS AND MULTIPLE DIVISORS GRAPHS | ||
| Pure and Engineering Sciences | ||
| Article 13, Volume 20, Issue 1, 2018, Pages 155-159 PDF (528.77 K) | ||
| DOI: 10.26682/sjuod.2018.20.1.14 | ||
| Authors | ||
| HARIWAN FADHIL M.SALIH; NECHIRVAN BADAL IBRAHIM | ||
| Dept. of Mathematics, College of Science University of Duhok, Kurdistan Region-Iraq. | ||
| Abstract | ||
| In this paper we introduce two new concepts of graphs. Let R be a commutative ring with identity and Z(R)\{0} be the set of elements in R divided it into two sets Z1(R) and Z2(R) , where Z1(R) be the set of co-prime divisor elements satisfies the Euler’s function and Z2(R) be the set of non-co-prime divisor elements, a simple graph MC(R) is associated to Z(R) it is called multiple co-prime divisors graph. Moreover, Let R be a commutative ring with identity and Z*(R)=Z(R)\{0} be the set of all non-zero divisor elements in R, a simple graph M(R) is associated to R for distinct elements a and b in Z*(R) is an edge in M(R) if and only if aba=a(mod n) for all n in N. Also, diameter, girth, chromatic number and nullity of multiple co-prime divisor and multiple divisor graphs will be determined. | ||
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