A longest sequence $ S $ of distinct vertices of a graph $ G $ such that each vertex of $ S $
dominates some vertex that is not dominated by its preceding vertices, is called a Grundy …

Assuming the existence of a partition in perfect codes of the vertex set of a finite or infinite
bipartite graph G we give the construction of a perfect code in the Cartesian product G□ G□ …

A graph is an efficient open (resp. closed) domination graph if there exists a subset of
vertices whose open (resp. closed) neighborhoods partition its vertex set. Graphs that are …

A vertex subset of a graph constitutes a 1-perfect code if the one-balls centered at the nodes
in effect a vertex partition of. This paper considers the quad-cube that is a connected-regular …

The commuting graph 𝒞 (Ω, G) of a finite group G has vertex set as Ω⊆ G, and any two
distinct vertices x, y are adjacent if x and y commute with each other. In this paper, we first …

The (non-)existence of perfect codes in Fibonacci cubes - ScienceDirect Skip to main
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Given a graph $ G $, a subset $ S $ of vertices of $ G $ is an efficient dominating set ($ EDS
$) if $| N [v]\cap S|= 1, $ for all $ v\in V (G) $. A graph $ G $ is efficiently dominatable if it …

A digraph D is an efficient closed domination digraph if there exists a subset S of V (D) for
which the closed out-neighborhoods centered in vertices of S form a partition of V (D). In this …

A k-king in a digraph D is a vertex that can reach every other vertex in D by a dipath of length
at most k. Here, we investigate the existence of k-kings in products of digraphs. We show …

A digraph D is an efficient open domination digraph if there exists a subset S of V (D) for
which the open out-neighborhoods centered in the vertices of S form a partition of V (D). In …