Total and forcing total edge-to-vertex monophonic number of a graph

J. John () and K. Uma Samundesvari ()
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J. John: Government College of Engineering
K. Uma Samundesvari: Noorul Islam Centre for Higher Education

Journal of Combinatorial Optimization, 2018, vol. 35, issue 1, No 11, 134-147

Abstract: Abstract For a connected graph $$G = \left( V,E\right) $$ G = V , E , a set $$S\subseteq E(G)$$ S ⊆ E ( G ) is called a total edge-to-vertex monophonic set of a connected graph G if the subgraph induced by S has no isolated edges. The total edge-to-vertex monophonic number $$m_{tev}(G)$$ m t e v ( G ) of G is the minimum cardinality of its total edge-to-vertex monophonic set of G. The total edge-to-vertex monophonic number of certain classes of graphs is determined and some of its general properties are studied. Connected graphs of size $$q \ge 3 $$ q ≥ 3 with total edge-to-vertex monophonic number q is characterized. It is shown that for positive integers $$r_{m},d_{m}$$ r m , d m and $$l\ge 4$$ l ≥ 4 with $$r_{m}

Keywords: Monophonic path; Monophonic set; Monophonic number; Edge-to-vertex monophonic set; Edge-to-vertex monophonic number; Forcing edge-to-vertex monophonic number; 05C12 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0160-y

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