Question

Let G, Km (m2 2) and G2 W, (n z 3), where G, and G2 |graphs. How many edges are in G, U G2 if G, and G2 have p (1 |sps min{m,n}) vertices in common one of which is the hub of the wheel and the rest are consecutive vertices along the wheel's circumference?

Km represents a complete graph and Wn represents wheels

Answer 1

> 2) and G2 Given that G Wa, (wheel graph with n > 3) such that p vertices are in common with atleast hub of G2 is in G Suppose e represents number of edges in a graph G. we know that m(m-1) and e, = 2n -- 2 K m(Complete graph with m 2 Also given that the p common vertices between Gi and G2 are con- secutive on the wheel of G2. Therefore the n-p vertices in G2 which are not in Gi are also consecutive on the wheel of G2. If p 1 edges of Gi and G2 are common, m(m-1)2n - 2 no eGiUG2 eG, + €G2. If p 1, m -p consecutive vertices on the wheel of G2 are not in G. The edges incident on them are n - p joining them to the hub and n - p1 to complete the wheel 2 number of edges of G2 that are not of Gi = m(m-1) 2(n - p) + 1. eG EGIUG2 m(m-1)n- p+n-p+1 2 2