Let G be an arbitrary graph with v nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie down between _____ and _____(a) n-1 and n+1(b) v and k(c) k+1 and v-k(d) k-1 and v-1The question was posed to me in an interview.My question is taken from Complete and Connected Graphs topic in section Graphs of Discrete Mathematics

Let G be an arbitrary graph with v nodes and k components. If a vertex

1.	Let G be an arbitrary graph with v nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie down between _____ and _____(a) n-1 and n+1(b) v and k(c) k+1 and v-k(d) k-1 and v-1The question was posed to me in an interview.My question is taken from Complete and Connected Graphs topic in section Graphs of Discrete Mathematics
Answer» Right option is (d) k-1 and v-1 Explanation: If a VERTEX is REMOVED from the graph, lower bound: number of components DECREASED by one = k-1 (remove an isolated vertex which was a COMPONENT) and upper bound: number of components = v-1 (CONSIDER a vertex connected to all other vertices in a component as in a star and all other vertices outside this component being isolated. Now, removing the considered vertex makes all other (v-1) vertices isolated making (v-1) components.

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