An independent set C of vertices in a graph is an efficient dominating set (or perfect code)
when each vertex not in C is adjacent to exactly one vertex in C. An E-chain is a countable …

A totally efficient coloring of a regular graph with color set formed by one unit more than its
degree is a total coloring in which each vertex color class is an efficient dominating set, that is …

AssrRAcr. We deal with a family of undirected Cayley graphs X. which are unions of disjoint
Hamilton cycles, and some of their properties, where rz runs over the positive integers. It is …

We show there is an uncountable number of parallel total perfect codes in the integer lattice
graph ${\Lambda}$ of $\R^2$. In contrast, there is just one 1-perfect code in ${\Lambda}$ …

Let $0<k\in\mathbb{Z}$. We zipper-merge integer compositions with sums $k$ and $k+1$,
equal number of parts and initial entries equal at least to 1 and 2, respectively. This yields …

… This generalizes Dejter-Serra work on vertex partitions of star Cayley graphs into EDSs. To
start with, the notion of EDS of a graph is generalized to that of an efficient dominating αset, …

A vertex subset $S$ of a graph $G$ is a perfect (resp. quasiperfect) dominating set in $G$ if
each vertex $v$ of $G\setminus S$ is adjacent to only one vertex ($d_v\in\{1,2\}$ vertices) of …

A sequence S of restricted-growth strings unifies the presentation of middle-levels graphs
Mk as follows, for 0< k∈ Z. Recall Mk is the subgraph in the Hasse diagram of the Boolean …

The existence of a connected 12-regular $\{K_4,K_{2,2,2}\}$-ultrahomogeneous graph $G$
is established, (ie each isomorphism between two copies of $K_4$ or $K_{2,2,2}$ in $G$ …

An infinite ordered tree $T$ exists that has as its vertex set a collection of tight restricted-growth
strings representing all Dyck words; these stand for the cyclic (resp., dihedral) classes …