Given a simple undirected graph G and a positive integer k, the k-forcing number of G,
denoted F k (G), is the minimum number of vertices that need to be initially colored so that all …

Let G be a graph and let k and j be positive integers. A subset D of the vertex set of G is a k-
dominating set if every vertex not in D has at least k neighbors in D. The k-domination …

Let G be a graph and let D be a subset of its vertex set. D is called k-dominating if| N (v)∩
D|≥ k for all v∈ V (G)∖ D; D is called k-tuple dominating if| N v∩ D|≥ k for all v∈ V (G); and …

The k-domination number of a graph is the cardinality of a smallest set of vertices such that
every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds …

A set S of vertices in a graph G is a 2-dominating set if every vertex of G not in S is adjacent
to at least two vertices in S. The 2-domination number γ 2 (G) is the minimum cardinality of a …

Abstract In 2014, Desormeaux et al.(Discrete Math 319: 15–23, 2014) proved a relationship
between the annihilation number and 2-domination number of a tree. In this note, we …

We introduce a procedure, called the Degree Sequence Index Strategy (DSI), by which to
bound graph invariants by certain indices in the ordered degree sequence. As an illustration …

TxGraffiti is an automated conjecturing program that produces graph theoretic conjectures in
the form of conjectured inequalities. This program written and maintained by the second …

The k-residue of a graph, introduced by Jelen in a 1999 paper, is a lower bound on the k-
independence number for every positive integer k. This generalized earlier work by Favaron …

In this paper we introduce and study a new graph invariant derived from the degree
sequence of a graph G, called the sub-k-domination number and denoted sub k (G). This …