More than ten years ago in 2008, a new kind of graph coloring appeared in graph theory,
which is the {\it rainbow connection coloring} of graphs, and then followed by some other …

A rainbow path in an edge-colored graph G is a path that every two edges have different
colors. The minimum number of colors needed to color the edges of G such that every two …

The proper rainbow vertex connection number of G, denoted by prvc (G), is the smallest
number of colors needed to properly color the vertices of G so that G is rainbow vertex …

Let (Γ,*) be a finite group with S={u∈ Γ| u= u− 1}, T={v∈ Γ| v≠ v− 1},| S|= 𝑠, and| T|= t. The
inverse graph of (Γ,*), denoted by IG (Γ), is a graph whose set of vertices is Γ such that two …

A path in an edge-colored graph G is called a rainbow path if no two edges on the path have
the same color. The graph G is called rainbow connected if between every pair of distinct …

A path in an edge-coloured graph is called\emph {rainbow path} if its edges receive pairwise
distinct colours. An edge-coloured graph is said to be\emph {rainbow connected} if any two …

A path in an edge-colored graph is called a rainbow path if every two distinct edges of the
path have different colors. A graph whose every pair of vertices are linked by a rainbow path …

The proper rainbow vertex connection number of G, denoted by prvc (G), is the smallest
number of colors needed to properly color the vertices of G to make G rainbow vertex …

A vertex-coloured graph G is said to be rainbow vertex-connected, if every two vertices of G
are connected by a path whose internal vertices have distinct colours. The rainbow vertex …

Pewarnaan-sisi pada graf G adalah suatu fungsi W∶ E (G)→{1, 2,…, k}=[k] di mana [k]
adalah himpunan warna. Pewarnaan-sisi-sejati pada graf G merupakan pewarnaan-sisi G …