the broadcast domination number of the cartesian product of two cycles is completely determined.

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

The well-known radial graph layout technique has plenty of advantages for graph visualization and graph exploration, but is quite limited in the size of graphs it can display effectively because the layout is inherently global and allows far away or out of view nodes to distort the focus region. The primary contribution of this project is to introduce sub tree clustering to allow the layout alg...

By an ortho-radial drawing of a graph we mean a planar drawing on concentric circles such that each edge is an alternating sequence of circular and radial segments, where a circular segment is a part of a circle and a radial segment is a part of a half-line starting at the center of the circles. Ortho-radial drawings are topologically an extension of orthogonal drawings to drawings on a cylinde...

A drawing of a graph G is radial if the vertices of G are placed on concentric circles C1, . . . , Ck with common center c, and edges are drawn radially: every edge intersects every circle centered at c at most once. G is radial planar if it has a radial embedding, that is, a crossing-free radial drawing. If the vertices of G are ordered or partitioned into ordered levels (as they are for level...

A drawing of a graph G is radial if the vertices of G are placed on concentric circles C1, . . . , Ck with common center c, and edges are drawn radially: every edge intersects every circle centered at c at most once. G is radial planar if it has a radial embedding, that is, a crossing-free radial drawing. If the vertices of G are ordered or partitioned into ordered levels (as they are for level...

We describe and discuss a novel radial version of a scalable dynamic graph visualization. The radial layout encodes dynamic directed graphs on narrow rings of a circle. The temporal evolution of the graph is mapped to rings that grow outward from the center of the circle. Graph vertices are placed equidistantly at the borderlines of each ring. Graph edges are displayed as curved lines starting ...

In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R∗(G) based on G has the vertex set a...

A level graph G = (V,E, λ) is a graph with a mapping λ : V → {1, . . . , k}, k ≥ 1, that partitions the vertex set V as V = V1 ∪ . . . ∪ Vk, Vj = λ−1(j), Vi ∩ Vj = ∅ for i ̸= j, such that λ(v) = λ(u) + 1 for each edge (u, v) ∈ E. Thus a level planar graph can be drawn with the vertices of every Vj , 1 ≤ j ≤ k, placed on a horizontal line, representing the level lj , and without crossings of edge...

We study orthogonal drawings of 4-planar graphs on cylinders—so called ortho-radial drawings. Equivalently these can be regarded as drawings on an ortho-radial grid formed by concentric circles and rays from the center of these circles but excluding the center itself. Ortho-radial drawings form a proper extension of orthogonal drawings in the plane. We present ortho-radial representations as a ...