Abstract Let G=(V, E) be a graph of order n and let B (D) be the set of vertices in V∖ D that
have a neighbor in the vertex set D. The differential of a vertex set D is defined as∂(D)=| B …

Let G=(V, E) be a simple graph with vertex set V and edge set E. Let D be a subset of V, and
let B (D) be the set of neighbours of D in V∖ D. The differential∂(D) of D is defined as| B …

Let G=(V, E) be a graph of order n and let B (D) be the set of vertices in V\D that have a
neighbor in the vertex set D. The differential of a vertex set D is defined as∂(D)=| B (D)|−| D …

We introduce the differential polynomial of a graph. The differential polynomial of a graph G
of order n is the polynomial B (G; x):= ∑ _ k=-n^ ∂ (G) B_k (G) x^ n+ k B (G; x):=∑ k …

The differential of D is defined as∂(D)=| B (D)|−| D| and the differential of a graph G,
written∂(G), is equal to max {∂(D): D⊆ V}. The Differential in Graphs, was introduced in …

Abstract Let G=(V, E) be a simple graph with vertex set V and edge set E. Let D be a subset
of V, and let B (D) be the set of neighbors of D in V∖ D. The differential∂(D) of D is defined …

Consider a simple graph Γ=(V (Γ), E (Γ)) with n vertices and m edges. Let P be a subset of V
(Γ) and B (P) the set of neighbors of P in V (Γ)\P. In the study of graphs, the concept of …

If G=(V (G), E (G)) is a simple connected graph with the vertex set V (G) and the edge set E
(G), S is a subset of V (G), and let B (S) be the set of neighbors of S in V (G)∖ S. Then, the …

Given a graph G and a subset of vertices D ⊆ V (G) D⊆ V (G), the external neighbourhood
of D is defined as N_e (D)={u ∈ V (G) ∖ D:\, N (u) ∩ D ≠\varnothing\} N e (D)= u∈ V (G)\D …

A graph is chordal if every induced cycle has exactly three edges. A vertex separator set in a
graph is a set of vertices that disconnects two vertices. A graph is δ-hyperbolic if every …