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A Note on "Monophonic Distance in Graphs"

In the paper entitled, "Monophonic Distance in Graphs", which appeared in Discrete Mathematics, Algorithms and Applications3(2) (2011) 159–169, it was proved (Theorem 3.4) that every graph is the monophonic center of some connected graph. Although the statement of the theorem is true, the proof given works only for graphs with monophonic diameter at most 2. Hence, we give a new proof of the same theorem, which works for all graphs. We settle completely the second part of Theorem 2.10(b) in that paper for all values a, b, c with 1 ≤ a ≤ b ≤ c, which also solves the Problem 2.12 given in that paper.