The Forcing Monophonic Hull Number of a Graph International Journal of Mathematical Trends and Technology (IJMTT) © 2012 by IJMTT Journal Volume-3 Issue-2 Year of Publication : 2012 Authors : J. John, V. Mary Gleeta J. John, V. Mary Gleeta "The Forcing Monophonic Hull Number of a Graph"International Journal of Mathematical Trends and Technology (IJMTT),V3(2):43-46.June 2012. Published by Seventh Sense Research Group.

Abstract
For a connected graph G = (V, E), let a set M be a minimum monophonic hull set of G. A subset T  M is called a forcing subset for M if M is the unique minimum monophonic hull set containing T. A forcing subset for M of minimum cardinality is a minimum forcing subset of M. The forcing monophonic hull number of M, denoted by fmh(M), is the cardinality of a minimum forcing subset of M. The forcing monophonic hull number of G, denoted by fmh(G), is fmh(G)=min{fmh(M)}, where the minimum is taken over all minimum monophonic hull sets in G. Some general properties satisfied by this concept are studied. The forcing monophonic hull numbers of certain classes of graphs are determined. It is shown that, for every pair a, b of integers with 0 ≤ a ≤ b and b ≥ 2, there exists a connected graph G such that fmh(G) = a and mh(G) = b.

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Keywords
hull number, monophonic hull number, forcing hull number, forcing monophonic hull number.