POLYNOMIAL ALGORITHM FOR FINDING A HAMILTONIAN CYCLE ON A GRAPH

On Szeged Polynomial of a Graph

On the Roots of Hosoya Polynomial of a Graph

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

SIMULATED ANNEALING ALGORITHM FOR SELECTING SUBOPTIMAL CYCLE BASIS OF A GRAPH

The cycle basis of a graph arises in a wide range of engineering problems and has a variety of applications. Minimal and optimal cycle bases reduce the time and memory required for most of such applications. One of the important applications of cycle basis in civil engineering is its use in the force method to frame analysis to generate sparse flexibility matrices, which is needed for optimal a...

Experimental Results on Hamiltonian-Cycle-Finding Algorithms

Frieze [1] introduced a heuristic polynomial-time algorithm, Ham, for finding Hamiltonian cycles in random graphs with high probability. We wanted to see how this algorithm performs in practice, and whether it could be improved by modifying it. For this purpose, we borrowed an idea from an algorithm by Keydar called SemiHam [2]. SemiHam is a modification of Ham that finds Hamiltonian cycles in ...

A Polynomial Time Algorithm for Graph Isomorphism

Algorithms testing two graphs for isomorphism known as yet in computer science have exponential worst case complexity. In this paper we propose an algorithm that has polynomial complexity and constructively supplies the evidence that the graph isomorphism lies in P.