In this paper, we show that every ( 3 k − ) -edge-connected graph G , under a certain degree condition, can be edge-decomposed into factors 1 … such for each vertex v ∈ V i | d / < where ≤ . As an application, deduce 6 three 2 and with unless has exactly one z ⁄ ≡ 0 Next, odd- have the same parity is odd positive integer Finally, give sufficient edge-connectivity condition to factor F specified...

A multigraph is exactly k-edge-connected if there are exactly k edgedisjoint paths between any pair of vertices. We characterize the class of exactly 3-edge-connected graphs, giving a synthesis involving two operations by which every exactly 3-edge-connected multigraph can be generated. Slightly modi ed syntheses give the planar exactly 3-edge-connected graphs and the exactly 3-edge-connected g...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

Mycielski introduced a new graph transformation μ(G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super-κ (resp. super edge connected or super-λ), if every minimum vertex cut (resp. minimum edge cut) isolates a vertex of G. In this paper, we show that for a connected graph G with |V (G)| ≥ 2, μ(G) is super-κ if and only if δ(G) < 2κ(G), and μ(G) is s...

The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994. However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.