THE RAINBOW CONNECTION NUMBER AND THE RAINBOW VERTEX CONNECTION NUMBER OF SPLITTING GRAPH OF SOME CLASSES OF GRAPH
if every two vertices in G are connected by a path whose edges have distinct colors. Such a path is called rainbow path. We denote rc(G), the rainbow connection number of G, as the smallest number of colors needed in order to make G rainbow connected. The vertex-colored graph G is said rainbow v...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/54951 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | if every two vertices in G are connected by a path whose edges have distinct colors.
Such a path is called rainbow path. We denote rc(G), the rainbow connection
number of G, as the smallest number of colors needed in order to make G rainbow
connected.
The vertex-colored graph G is said rainbow vertex-connected if any two vertices
in G are connected by a path whose all internal vertices have different colors.
Such a path is called rainbow vertex-path. The rainbow vertex-connection number,
denoted by rvc(G), is the smallest number of colors needed such that G is rainbow
vertex-connected.
For a graph G, the splitting graph Sl(G) of graph G is obtained by adding |V (G)|
new vertices on G such that for each vertex u of a graph G we have a new vertex u0
then joining u0 to all vertices of G that adjacent to u.
In this thesis, we provide lower and upper bound of the rainbow connection number
and the rainbow vertex connection number of splitting graph. For rainbow connection
number, we determine the rc of splitting graph of some graph classes, such as
path graph, star graph, fan graph, friendship graph and wheel graph. For rainbow
connection vertex number, we give the rvc of splitting graph of some graph classes
based on its diameter. |
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