A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195200) proved that the Hamiltonian Cycle Problem is NP-Complete even for undirected path graphs and left the Hamiltonian cycle problem open for directed path graphs. Narasimhan (1989, Information Processing Letters, 32, 167-170) proved tha...

The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is O(n). Abstract. Hamiltonian Cycle, Z-mapping graph, complexity, decision, matching covered, optimization Hamiltonian Cycle, Z-mapping graph, complexity, decision, matching covered, optimization

A Hamiltonian cycle in a graph G is a simple cycle in which each vertex of G appears exactly once. The Hamiltonian cycle problem involves testing whether a Hamiltonian cycle exists in a graph, and finds one if such a cycle does exist. It is well known that the Hamiltonian cycle problem is one of the classic NP-complete problems on general graphs. Shih et al. solved the Hamiltonian cycle problem...

It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP -hard in general, and no polynomial time algorithm is known for the problem of finding a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the complexity of approximating this problem where by a feasible solution we mean a(nother) cycle in t...

We say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturat...

Suppose we have some undirected graph G = (GV , GE) represented as an adjacency matrix with |GV | rows and |GV | columns. G is said to be Hamiltonian if there exists a cycle CH that passes through each vertex in GV exactly once. This cycle is called a Hamiltonian cycle. Finding a Hamiltonian cycle in a graph if one exists is an NP-complete problem. We would like to use a zeroknowledge protocol ...