ON THE LOCATING RAINBOW CONNECTION NUMBER FOR CORONA PRODUCT OF GRAPHS
Let k be a positive integer and G = (V;E) be a finite and connected graph. A path P of G whose all internal vertices have distinct colors is called a rainbow vertex path. A vertex k-coloring of G is function c : V (G) ! f1; 2; ; kg such that for every u and v in V (G) there exists a rainbow ve...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/53761 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let k be a positive integer and G = (V;E) be a finite and connected graph. A path
P of G whose all internal vertices have distinct colors is called a rainbow vertex
path. A vertex k-coloring of G is function c : V (G) ! f1; 2; ; kg such that for
every u and v in V (G) there exists a rainbow vertex path that connects them. For
i 2 f1; 2; ; kg, let Ri be a set of vertex with color i and = fR1;R2; : : : ;Rkg
be an ordered partition of V (G). The rainbow code of a vertex v 2 V (G) with
respect to is defined as the k-tuple rc(v) = (d(v;R1); d(v;R2); : : : ; d(v;Rk))
with d(v;Ri) = minfd(v; y)jy 2 Rig for i 2 f1; 2; ; kg. If every vertex of G has
distinct rainbow codes, then c is called a locating rainbow k-coloring of G. The
locating rainbow connection number of G, denoted by rvcl(G), is defined as the
smallest positive integer k such that G has a locating rainbow k-coloring.
In this thesis, we give a lower bound and an upper bound for the locating rainbow
connection number of corona product of a connected graph G with a graph H.
Furthermore, we determine the locating rainbow connection number of corona product
of any connected graph G with a graph H, where H is the complement of a
complete graph, a complete graph, or a star graph. |
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