RAMSEY NUMBER FOR PAIR OF STAR GRAPH WITH DUMBBELL GRAPH
The star graph K1,p?1 is a connected graph that has one vertex of degree p?1 and all other vertices of degree 1. The dumbbell graph Dn,m is the complete graph Kn and Km that are mutually exclusive with exactly a pair of adjacent vertices (vp,vm), vp ? Kp,vm ? Km. Let G,G1,G2 be simple graphs. The...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/73200 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The star graph K1,p?1 is a connected graph that has one vertex of degree p?1 and
all other vertices of degree 1. The dumbbell graph Dn,m is the complete graph Kn
and Km that are mutually exclusive with exactly a pair of adjacent vertices (vp,vm),
vp ? Kp,vm ? Km. Let G,G1,G2 be simple graphs. The Ramsey number R(G1,G2)
denotes the smallest integer n such that for every simple graph G with n vertices, either
G1 ? G or G2 ? G. In this final project, we determine the values of the Ramsey
number for pairs of star graphs with barbell graphs, R(K1,p?1,Dn,m), for every p ? 2,
3 ? n ? m, where p,n,m are natural numbers. |
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