Let G = (V, E) be a simple connected graph, then the basis number of is denoted by b(G) and defined least positive integer k such that graph has − fold for it cycle space. In this paper we studied Mycielski’s some cog-special graphs, compute cog-path cog-cycle cog-star cog-wheel graph.

We build unbounded classes of plane and projective plane multiwheels that are 4-critical that are received summing odd wheels as edge sums modulo two. These classes can be considered as ascending from single common graph that can be received as edge sum modulo two of the octahedron graph O and the minimal wheel W3.

In this paper, using a well-known recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multi-bridge graph and some 2−tree graphs. Further, several recursive formulae for other graphs such as the fan and the wheel graphs are also discussed.

The chain theorem of Tutte states that every 3-connected graph can be constructed from a wheel Wn by repeatedly adding edges and splitting vertices. It is not difficult to prove the following strengthening this theorem: non-wheel W4 In paper, we similarly strengthen several theorems for various versions 4-connectivity.

We present the first polynomial time construction procedure for generating graceful double-wheel graphs. A graph is graceful if its vertices can be labeled with distinct integer values from {0, ..., e}, where e is the number of edges, such that each edge has a unique value corresponding to the absolute difference of its endpoints. Graceful graphs have a range of practical application domains, i...

Chemical compounds and drugs are often modelled as graphs (for example, Polyhex Nanotubes and Dendrimer Nanostar) where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph and can be different structures. The edge Wiener index of ...

I.Cahit introduced cordial graphs as a weaker version of graceful and harmonious graphs. The total product cordial labeling is a variant of cordial labeling. In this paper we introduce a vertex analogue product cordial labeling as a variant of total product cordial labeling and name it as total vertex product cordial labeling. Finally, we investigate total vertex product cordial labeling for ma...

The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly

We study biplane graphs drawn on a finite point set S in the plane in general position. This is the family of geometric graphs whose vertex set is S and which can be decomposed into two plane graphs. We show that every sufficiently large point set admits a 5-connected biplane graph and that there are arbitrarily large point sets that do not admit any 6connected biplane graph. Furthermore, we sh...