In this paper two linear arrays including a linear 1×4 and a planar 2×2 of microstrip patch and half-mode substrate integrated waveguide (SIW) cavity hybrid antenna are introduced and investigated. These are simply implemented using low cost single layer printed circuit board (PCB) process. The array element consists of a rectangular microstrip patch with appropriate dimensions in the vicinity ...

An (m,n)-colored-mixed graph G=(V,A1,A2,⋯,Am,E1,E2,⋯,En) is a having m colors of arcs and n edges. We do not allow two or edges to have the same endpoints. A homomorphism from an G another H morphism φ:V(G)→V(H) such that each edge (resp. arc) mapped color (and orientation). T said be Pg(m,n)-universal if every in Pg(m,n) (the planar graphs with girth at least g) admits T. show exist for 2m+n≥3...

We prove that we can specify by formulas of monadic second-order logic the unique planar embedding of a 3-connected planar graph. If the planar graph is not 3-connected but given with a linear order of its set of edges, we can also define a planar embedding by monadic second-order formulas. We cannot do so in general without the ordering, even for 2-connected planar graphs. The planar embedding...

Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field K that induce planar functions on infinitely many extensions of K; we call such polynomials exceptional planar. Exceptional planar monomials have been recently classified. In this paper we establish a partial...

Extending the concept of ordered graphs, we propose a new data structure to express rooted planar maps, which is called a planar map pattern. In order to develop an efficient data mining method from a dataset of rooted planar maps, we propose a polynomial time algorithm for finding a minimally generalized planar map pattern, which represents maximal structural features common to rooted planar m...

This paper is dedicated to propose an algorithm in order to generate the certain isomers of some well-known fullerene bases. Furthermore, we enlist the bipartite edge frustration correlated with some of symmetrically distinct innite families of fullerenes generated by the oered process.