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Let G1 = (V, E1) and G2 = (V, E2)  be connected graphs on the same vertex set V with more than two vertices. If   G1 ∩ G2  = (V, E∩ E2 )  is not a connected graph, then the graph G1 ∪ G2  = (V, E∪ E2 )
  • a)
    cannot have a cut vertex
  • b)
    must have a cycle
  • c)
    must have a cut-edge (bridge)
  • d)
    Has chromatic number strictly greater than those of G1 and G2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let G1= (V, E1) and G2= (V, E2) be connected graphs on the same vertex...
Take a tree for example
(A) False. Every vertex of tree(other than leaves) is a cut vertex
(B)True
(C)False. Without E in G1 and G2, G1 U G2 has no bridge.
(D)False. G1 U G2, G1, G2 three graphs have same chromatic number of 2.
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Most Upvoted Answer
Let G1= (V, E1) and G2= (V, E2) be connected graphs on the same vertex...
Has more edges than G2 (i.e., |E1| > |E2|), then G1 cannot be a tree.
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Let G1= (V, E1) and G2= (V, E2) be connected graphs on the same vertex set Vwith more than two vertices. If G1∩ G2 = (V, E1∩ E2) is not a connected graph, then the graphG1∪ G2 = (V, E1∪ E2)a)cannot have a cut vertexb)must have a cyclec)must have a cut-edge (bridge)d)Has chromatic number strictly greater than those of G1and G2Correct answer is option 'B'. Can you explain this answer?
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