RAMSEY NUMBER FOR PAIR OF STAR GRAPH WITH DUMBBELL GRAPH - Bimo Rizqullah, Sulthan
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.