and, for two distinct

vertices x and y, there is an arc from x to y if and only if xy = α(y)x + b(y). We study

some basic properties of ΓR(α, b). Also, we investigate the planarity and genus of the

graph ΓR(α, 0)....

of Gamma^n_R. We also determine all isomorphic

classes of finite commutative rings whose generalized Cayley graph

has genus at most three....

investigate

the planarity, outerplanarity and ring graph of Cay^+(I(R); S ) and also we provide some characterization

for rings R whose Cayley sum graphs have genus one....

After a short review on taxonomic contributions to Iranian Allium species after-Flora Iranica-(1971), Allium longipapillatum R.M. Fritsch & Matin, A. montelburzense R.M. Fritsch, Y. Salmaki & SH. Zarre, and A. kuhsorkhense ...

to J, whenever I contains

a non-zero divisor on J. In this paper, we investigate the planarity

of \\gama(R). We also completely characterize the rings R such that

\\gama(R) is a ring graph, and the situations under which the genus...

According to the literatures,

Zarudny’s bird collection from Iran (Persia) is

scattered in several museums all over the world.

Taxonomy and biogeography of Remiz genus

is in the shadow and there is no information...

^n_R.

We also determine all isomorphic classes of finite commutative rings whose

generalized zero divisor graphs have genus at most three....

Genus Rattus from the subfamily Murinae has a wide geographical distribution

throughout the world. Three species of this genus have been reported in Iran so far. They

are Norway or brown rat ( Rattus norvegicus ), black rat (Rattus...