Let G be a graph. The core of G, denoted by G ∆ , is the subgraph of G induced by the vertices of degree ∆(G), where ∆(G) denotes the maximum degree of G. A k-edge coloring of G is a function f : E(G) → L such that |L| = k and f (e 1) = f (e 2) for all two adjacent edges e 1 and e 2 of G. The chromatic index of G, denoted by χ (G), is the minimum number k… (More)
Let G and H be two graphs. A proper vertex coloring of G is called a dynamic coloring, if for every vertex v with degree at least 2, the neighbors of v receive at least two different colors. The smallest integer k such that G has a dynamic coloring with k colors denoted by χ 2 (G). We denote the cartesian product of G and H by GH. In this paper, we prove… (More)
In this paper, we consider variational iteration method (VIM) to obtain exact solution to the Fisher's equation. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a functional. Using this method, it is possible to find the exact solution or an approximate solution of the problem.
In this paper, by considering the variational iteration method, a kind of explicit exact and numerical solutions to the Lienard equation is obtained, and the numerical solutions has been compared with their known theoretical solution. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a… (More)