This paper describes the methods using bonded cup wheels for grinding toroidal and cylindrical SiC mirrors with large curvature radii. Since the angle between the cutting direction of bonded abrasives and feed direction of the cup wheel is about 90 °, it is possible to obtain a surface with very low surface roughness independent of the direction of measurement. Toroidal mirrors, circular and el...

For a set S of vertices and the vertex v in a connected graph G, max x∈S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −...

The cycle matroids of wheels are the fundamental building blocks for the class of binary matroids. Brylawski has shown that a binary matroid has no minor isomorphic to the rank-3 wheel M(1f3) if and only if it is a series-parallel network. In this paper we characterize the binary matroids with no minor isomorphic to M (if;.). This characterization is used to solve the critical problem for this ...

In the context of formal deformation quantization, we provide an elementary argument showing that any universal quantization formula necessarily involves graphs with wheels.

A graph G = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y, x 6= y, alternate in w if and only if (x, y) ∈ E. Halldórsson, Kitaev and Pyatkin have shown that a graph is word-representable if and only if it admits a so-called semi-transitive orientation. A corollary of this result is that any 3-colorable graph is wordrepresentable.Masárová Akro...

For two given graphs F and H, the Ramsey number R(F,H) is the smallest positive integer p such that for every graph G on p vertices the following holds: either G contains F as a subgraph or the complement of G contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Wm), where Pn is a path on n vertices and Wm is the graph obtained from a cycle on m vertices by adding a new ver...

A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...

For n ∈ N and 3 ≤ k ≤ n we compute the exact value of Ek(n), the maximum number of edges of a simple planar graph on n vertices where each vertex bounds an l-gon where l ≥ k. The lower bound of Ek(n) is obtained by explicit construction, and the matching upper bound is obtained by using Integer Programming (IP.) We then use this result to conjecture the maximum number of edges of a non-flowerab...

A simple undirected graph G is called a sum graph if there exists a labelling L of the vertices of G into distinct positive integers such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label L(w) = L(u) + L(v). It is obvious that every sum graph has at least one isolated vertex, namely the vertex with the largest label. The sum number (H) of a ...