The neighborhood polynomial of graph $G$ is the generating function for number vertex subsets which vertices have a common neighbor in $G$. In this paper, we investigate behavior under several operations. Specifically, provide an explicit formula obtained from given by attachment. We use result to propose recursive algorithm calculation polynomial. Finally, prove that can be found polynomial-ti...

In this paper, we first collect the earlier results about some graph operations and then we present applications of these results in working with chemical graphs.

let g be a graph. the first zagreb m1(g) of graph g is defined as: m1(g) = uv(g) deg(u)2. in this paper, we prove that each even number except 4 and 8 is a first zagreb index of a caterpillar. also, we show that the fist zagreb index cannot be an odd number. moreover, we obtain the fist zagreb index of some graph operations.

The list coloring of a graph G = G(V, E) is to color each vertex v ∈ V (G) from its set L(v). If any two adjacent vertices have different colors, then properly colored. aim this paper study the some operations