Abstract. We will determine all infinite 2-locally finite groups and all infinite 2-groups

with planar subgroup graph, and show that infinite groups that satisfy the chain conditions

and contain an involution do not have planar embeddings...

.We denote this graph by

T_S(L). We study some properties of T_S(L).Moreover, we investigate the planarity of

T_S(L), whenever S is a saturated multiplicatively closed subset of L....

The design of an optical waveguide coupler has several challenges, such as reflection losses at the interfaces of the coupler, material complexity for optical applications, and the coupling between arbitrary materials at ...

if and only if a not in RB and b not in RA where for C in R RC is the ideal generated by c. In this paper we completely determine all finite commutative rings R such that \\gama'(R) is planar, outerplanar and ring gragh....

A dye molecule based on the bacteriochlorin (Bacteriochlorins are planar, highly conjugated macrocyclic molecules [1]), LS-01, as a sensitizer in the dye-sensitized solar cells (DSSCs) has been investigated. This molecule has a D-π-A architecture...

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)....

for total graphs. In this paper, we investigate the basic properties of GT^n_U (R^n). Moreover, we study the planarity of the graphs GT^n_U (U), GT^n_U (R^n-U) and GT^n_U (R^n)....

In this paper, we introduce and study a new class of Cayley graphs.