THE 4-RAINBOW INDEX OF CM + PN
Let G be a simple and connected graph of order n with an h-edge coloring c : E(G) ! f1; 2; : : : ; hg for some h 2 N, where adjacent edges may be colored the same. A tree T in G is called a rainbow tree, if no two edges of T have the same color. An h-edge coloring of G is called a k-rainbow h-edg...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/61244 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G be a simple and connected graph of order n with an h-edge coloring c :
E(G) ! f1; 2; : : : ; hg for some h 2 N, where adjacent edges may be colored the
same. A tree T in G is called a rainbow tree, if no two edges of T have the same
color. An h-edge coloring of G is called a k-rainbow h-edge coloring for some
k 2 f2; 3; : : : ; ng, if for every S V (G) with j S j= k, there exists a rainbow tree
in G containing the vertices of S. Such a rainbow tree is called a rainbow S????tree.
The k-rainbow index of G, denoted by rxk, is the minimum positive integer h such
that there is a k-rainbow h-edge coloring of G.
Let G1 = (V1;E1) and G2 = (V2;E2) be two graphs. The join of G1 and G2, denoted
by G1 + G2, is a graph with the vertex set V (G1 + G2) = V (G1) [ V (G2)
and the edge set E(G1 + G2) = E(G1) [ E(G2) [ fuv j u 2 V G1; v 2 V (G2)g.
In this thesis, we consider the 4-rainbow index of Cm+Pn for anym 3 and n 1. |
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