Global Journal of Theoretical and Applied Mathematics Sciences

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The Forcing Connected Edge Monophonic Number of a Graph


Affiliations
1 Alagappa Government Arts College, Karaikudi–630 003, India
2 Department of Mathematics, Government College of Engineering, Tirunelveli - 627007, India
     

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Let M be a minimum connected edge monophonic set of G. A subset T ⊆ M is called a forcing subset for M if M is the unique minimum connected edge monophonic set containing T. A forcing subset for M of minimum cardinality is a minimum forcing subset of M. The forcing connected edge monophonic number of M, denoted by fm1c(M), is the cardinality of a minimum forcing subset of M. The forcing connected edge monophonic number of G, denoted by fm1c(G), is fm1c(G) = min{fm1c(M)}, where the minimum is taken over all minimum connected edge monophonic set M in G. It is shown that for every integers a and b with a < b, and 􀜾 − 2􀜽 − 2 > 0, there exists a connected graph G such that, fm1c(G) = a and m1c(G) = b , where m1c (G) is the connected edge monophonic number of a graph G.

Keywords

Monophonic Number, Connected Edge Monophonic Number, Forcing Edge Monophonic Number, Forcing Connected Edge Monophonic Number
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  • The Forcing Connected Edge Monophonic Number of a Graph

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Authors

P Arul Paul Sudhahar
Alagappa Government Arts College, Karaikudi–630 003, India
J. John
Department of Mathematics, Government College of Engineering, Tirunelveli - 627007, India

Abstract


Let M be a minimum connected edge monophonic set of G. A subset T ⊆ M is called a forcing subset for M if M is the unique minimum connected edge monophonic set containing T. A forcing subset for M of minimum cardinality is a minimum forcing subset of M. The forcing connected edge monophonic number of M, denoted by fm1c(M), is the cardinality of a minimum forcing subset of M. The forcing connected edge monophonic number of G, denoted by fm1c(G), is fm1c(G) = min{fm1c(M)}, where the minimum is taken over all minimum connected edge monophonic set M in G. It is shown that for every integers a and b with a < b, and 􀜾 − 2􀜽 − 2 > 0, there exists a connected graph G such that, fm1c(G) = a and m1c(G) = b , where m1c (G) is the connected edge monophonic number of a graph G.

Keywords


Monophonic Number, Connected Edge Monophonic Number, Forcing Edge Monophonic Number, Forcing Connected Edge Monophonic Number

References