Let G be a simple graph with vertex set V (G) and edge set E (G). For x∈ V (G), let NG
(x)={y∈ V (G)| xy∈ E (G)} and NG (X)=⋃ x∈ XNG (x). For X⊆ V (G), the number d (X)≔| X …

We study the following problem: for given integers d, k and graph G, can we reduce some
fixed graph parameter π of G by at least d via at most k graph operations from some fixed set …

Abstract A set S ⊆ VS⊆ V is independent in a graph G=\left (V, E\right) G= V, E if no two
vertices from S are adjacent. The independence number α (G) α (G) is the cardinality of a …

Let G be a simple graph with the vertex set V (G) and edge set E (G). For x∈ V (G), let N
(x)={y∈ V (G)| xy∈ E (G)} and N (X)=⋃ x∈ XN (x). For X⊆ V (G), let d (X):=| X|-| N (X)| be the …

Let G be a simple graph with vertex set V G. A set A⊆ VG is independent if no two vertices
from A are adjacent. If α G+ μ G=| VG|, then G is called a König–Egerváry graph (Deming …

Let $ G $ be a simple graph with vertex set $ V (G) $. A set $ S\subseteq V (G) $ is
independent if no two vertices from $ S $ are adjacent. For $ X\subseteq V (G) $, the …

Let d and k be two given integers, and let G be a graph. Can we reduce the independence
number of G by at least d via at most k graph operations from some fixed set S? This …

Abstract Let G=(V, E) be a graph. A set I ⊆ V is independent if no two vertices from I are
adjacent, and by Ind (G) we mean the family of all independent sets of G, while core (G) is …

Let $\alpha (G) $ denote the cardinality of a maximum independent set, while $\mu (G) $ be
the size of a maximum matching in $ G=\left (V, E\right) $. Let $\xi (G) $ denote the size of the …

Let G be a finite simple graph. For X⊂ V (G), the difference of X, d (X)≔| X|−| N (X)| where N
(X) is the neighborhood of X and max {d (X): X⊂ V (G)} is called the critical difference of G. X …