The Detour Monophonic Convexity Number of a Graph

M Sivabalan, S Sundar Raj, V Nagarajan


A set  is detour monophonic convexif  The detour monophonic convexity number is denoted by  is the cardinality of a maximum proper detour monophonic convex subset of  Some general properties satisfied by this concept are studied. The detour monophonic convexity number of certain classes of graphs are determined. It is shown that for every pair of integers   and  with  there exists a connected graph  such that   and , where  is the monophonic convexity number of G


convex, detour, chord, detour monophonic path, monophonic convexity number, detour monophonic, convexity number.

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F. Buckley and F. Harary, Distance in Graphs, Addition-Wesley, Redwood City, CA, 1990.

G. Chartrand, G. Johns and S. Tian, Detour Distance in Graphs, Annals of Discrete Mathematics,55, 127-136, 1993.

G. Chartrand, C. Wall and P. Zhang, The Convexity number of a Graph, Graphs and Combinatorics, 18, 209-217, 2002.

G. Chartrand, G. Johns and P. Zhang, The detour number of a graph, Utilitas Mathematica, 64, 97-113, 2003.

P. Duchlet, Convex sets in Graphs, II. Minimal path convexity, J. Comb. Theory ser-B,44, 307-316, 1988.

J. John and S. Panchali, The upper monophonic number of a graph, International J. Combin, 4, 46-52,2010.

Jase Caceres and Ortrud R. Oellermann, Minimal Trees and Monophonic Convexity Discussiones Mathematicae Graph Theory, 32, 685-704,2012.

Mitre C. Dourado, Fabio Protti and Jayme L. Szwarcfiter, Complexity results related to monophonic convexity, Discrete Applied Mathematics, 158, 1268-1274. 2010.

S. V. Padmavathi, The Weak (Monophonic) convexity number of a graph, Progress in Nonlinear Dynamics and chaos, 3(2), 71-79,2015.

A. P. Santhakumaran and P. Titus, Monophonic distance in graphs, Discrete Mathematics, Algorithms and Applications, 3(2), 159 – 169,2011.

P. Titus, K. Ganesamoorthy and P. Balakrishnan, The detour monophonic number of a graph, ARS Combinatoria, 84, 179-188,2013.



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