We derive recurrence relations from partial differential equations whose formal power series solutions are the exponential generating functions for labeled, general cubic graphs with given connectedness. The relations are used to compute number of these graphs with a specified number of loops and multiple edges. In this paper, using the reduction method, we study the relationships between the Hamiltonian index and the diameter of a graph. This improves and extends several known results. Antiweb-wheel inequalities and their separation problems over the stable set polytopes.
G is a set of pairwise nonadjacent vertices.
The problem of finding a maximum weight stable set is one of the most basic NP-hard problems. Some known large classes of separable inequalities are the trivial, edge, cycle, and wheel inequalities. We also give efficient separation algorithms for them. This number exists if and only if G 1 is a star or G 2 is a forest. We consider a variety of upper and lower bounds for different classes of graphs and define several variations on this number.