Let R be a commutative ring and let Γ(Z n) be the zero divisor graph of a commutative ring R, whose vertices are non-zero zero divisors of Z n , and such that the two vertices u, v are adjacent if n divides uv. In this paper, we evaluate the changing and unchanging domination number of Γ(Z n) and we evaluate the same result in Γ(Z 2p), Γ(Z 3p), Γ(Z p 2),… (More)
In this paper, we evaluate the connected domination number of (Z n), in some case of n. We find out that the connected domination number of (Z p e 1 1 ×p e 2 2 ×···×p e k k) is equal to k. Finally, we characterize the graphs in which γ ((Z n)) = γ c ((Z n)).
Ewing's sarcoma/peripheral primitive neuroectodermal tumor is a small, round, and blue cell malignancy that occurs most often in bone and soft tissues of children and young adults. The intraspinal manifestation of the disease is rare, and when present, this is often misdiagnosed with other varieties of primary spinal tumors. Fine-needle aspiration cytology… (More)
reproduction in any medium, provided the original work is properly cited. Abstract A path double cover of a graph G is a collection of paths in G such that every edge of G belongs to exactly two paths in. The minimum cardinality of a path double cover is called the path double covering number of G and is denoted by PD G .In this paper we determine the… (More)
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we evaluate b(Γ(Z n)). Our main result is, we give maximum value of b(Γ(Z n)) is 0.99999999796427626489236243072661, where n is any positive integer upto fiftieth… (More)