Topics concerning metric dimension related invariants in graphs are nowadays intensively
studied. This compendium of combinatorial and computational results on this topic is an …

It is the origin of the Four Color Problem by Francis Guthrie in 1852 that led to coloring maps
and then to coloring planar graphs—not only coloring its regions but coloring its vertices and …

Let G be a connected graph. For a vertex v∈ V (G) and an ordered k-partition Π={S1, S2,...,
Sk} of V (G), the representation of v with respect to Π is the k-vector r (v| Π)=(d (v, S1), d (v …

On the partition dimension of unicyclic graphs Page 1 Bull. Math. Soc. Sci. Math. Roumanie
Tome 57(105) No. 4, 2014, 381-391 On the partition dimension of unicyclic graphs by Penning …

Let G=(V (G), E (G)) be a graph with no loops, numerous edges, and only one component,
which is made up of the vertex set V (G) and the edge set E (G). The distance d (u, v) …

For a nontrivial connected graph G, let c: V (G)→ N be a vertex coloring of G where adjacent
vertices may be colored the same and let V1, V2,..., Vk be the resulting color classes. For a …

Complex networks are difficult to understand and deal with, yet building a graph of any
complex and huge structure, whether chemical or computer-related, is quite straightforward …

Abstract Let G=(V, E) be a connected graphs with vertex set V (G), edge set E (G) and S⊆ V
(G). For an ordered partition Π={S 1, S 2, S 3,..., S k} of V (G), the representation of a vertex …

Misalkan G adalah sebuah graf nontrivial dan terhubung dengan himpunan simpul V (G),
himpunan sisi E (G) dan S⊆ V (G) dengan simpul v∈ V (G), jarak antara v dan S adalah d …

Let all graphs be a connected and simple graph. A set W={w 1, w 2, w 3,..., wk} of veretx set
of G, the k− vector ordered $ r (v| W)=(d (x,{w} _ {1}), d (x,{w} _ {2}),\ldots,\, d (x,{w} _ {k})) $ of …