Exact Formulae for the Lova'sz Theta Function of Sparse Circulant Graphs

Exact formulae for the Lovász Theta Function of sparse Circulant Graphs

Generalized Degree Distance of Strong Product of Graphs

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

Total and fractional total colourings of circulant graphs

In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional total chromatic number and for 4-regular circulant graphs we find the total chromatic number for some cases and we give the exact value of the fractional total chromatic number in most cases.

On the Lovász Number of Certain Circulant Graphs

The theta function of a graph, also known as the Lovv asz number, has the remarkable property of being computable in polynomial time, despite being \sandwiched" between two hard to compute integers, i.e., clique and chromatic number. Very little is known about the explicit value of the theta function for special classes of graphs. In this paper we provide the explicit formula for the Lovv asz n...

Analytical Enumeration of Circulant Graphs with Prime-Squared Number of Vertices

A method for the analytical enumeration of circulant graphs with p2 vertices, p a prime, is proposed and described in detail. It is based on the use of S-rings and P olya's enumeration technique. Two di erent approaches, \structural" and \multiplier", are developed and compared. As a result we get counting formulae and generating functions (by valency) for non-isomorphic p2-vertex directed and ...