The Forcing Monophonic Hull Number of a Graph
Journal Title: INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY - Year 2012, Vol 3, Issue 2
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.
Authors and Affiliations
J. John#1 , V. Mary Gleeta*2
Keywords
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