… We study domination between different types of walks connecting two non-adjacent vertices
u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in …

… A Lucas string Bn of length n is a binary string b1b2b3 ···bn containing no two consecutive …
the concept of a domination set in a graph. The concept of the domination in graphs provides …

… We will investigate dominating sets of path. We need the following lemmas to prove our … set
of G must contain at least k vertices of the path. To find a dominating set of P n with cardinality …

… a path or on a cycle, we come across two special partially dominated paths. Let Pn denote a
partially dominated path of … By Pn we denote a partially dominated path of order n + 1 where …

… If G is a domination critical graph with y(G) = k we will say G … ] and is a direct consequence
of considering the domination … contains a tournament, there is a spanning directed path for s. …

… We define a 3-path dominating set of G to be D = {Q1, Q2,..., Qk | Qi is a 3-path} such that …
We define a 3-path dominating set of G to be a set D = {Q1, Q2,..., Qk} of 3-paths such that the …

… a related minimization problem for which we find a lower bound. A graph G is an exact n-step
domination … Let v 0 ,v 1 ,…,v 2n−1 form a path belonging to a diameter of G. For each v i in …

… We also show that in a connected n-vertex graph having a dominating path, the lengths of …
In the introduction, we noted that a graph G with a dominating path has dominating paths of all …

… domination integrity of a simple connected graph is one such measure. Here we determine
the domination integrity of square graph of path as … domination integrity of a square graph of n …

… In general, for an edge 𝑢𝑣 ∈ 𝐸 to be subdivided 𝑘 ≥ 1 times, we mean that edge 𝑢𝑣 is
removed and replaced by a (𝑢, 𝑣)-path of length 𝑘 +1. The subdivision graph 𝑆(𝐺) is the graph …