On the upper open detour monophonic number of a graph
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Abstract
An open detour monophonic set $M$ in a connected graph $G$ is called a minimal open detour monophonic set if no proper subset of $M$ is an open detour monophonic set of $G$. The upper open detour monophonic number $\operatorname{odm}^{+}(G)$ of $G$ is the maximum cardinality of a minimal open detour monophonic set of $G$. Some general properties satisfied by this concept are studied. The upper open detour monophonic number of some standard graphs are determined. Connected graphs of order $n$ with upper open detour monophonic number 2 or 3 or $n$ are characterized. It is shown that for every pair $a$ and $b$ of integers $a$ and $b$ with $2 \leq a \leq b$, there exists a connected graph $G$ such that $o d m(G)=a$ and $o d m^{+}(G)=b$, where $o d m(G)$ is the open detour monophonic number of a graph.
Keywords:
detour number, open detour number, monophonic number, open monophonic number, upper open detour monophonic numberMathematics Subject Classification:
Mathematics- Pages: 765-769
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
M. C. Dourado, Fabio Protti and Jayme. L. Szwarcter, Algorithmic aspects of mono- phonic convexity, Electronic Notes in Discrete Mathematics, 30, (2008), 177 - 182.
F. Harary. Graph Theory. Addison-Wesley, 1969.
J. John and S. Panchali, The upper monophonic number of a graph, Int. J. Math. Combin. 4, (2010), $46-52$
J. John, P. Arul Paul Sudhahar and A. Vijayan, The connected monophonic number of a graph, International Journal of Combinatorial Graph Theory and Applications, 5(1), (2012), 83-90.
J. John ,P. Arul Paul Sudhahar and A. Vijayan, The connected edge monophonic number of a graph, Journal of Computer and Mathematical Sciences, 3 (2), (2012), $131-136$.
J. John and S. Panchali, The forcing monophonic number of a graph, IJMA-3 (3), (2012), 935-938.
J. John and K.U. Samundeswari, The forcing edge fixing edge-to-vertex monophonic number of a graph, Discrete Math. Algorithms Appl., 5(4), (2013), 1 - 10 .
J. John and K.U. Samundeswari, The edge fixing edgeto-vertex monophonic number of a graph, Appl. Math. E-Notes, 15, (2015), $261-275$.
J. John and K.U. Samundeswari, Total and forcing total edge-to-vertex monophonic numbers of graph, J. Comb. Optim., 34, (2017), $1-14$.
J. John, D. Stalin and P. Arul Paul Sudhahar, On the (M,D) number of a graph, Proyecciones Journal of Mathematics, 38 (2),(2019), 255-266,
J. John, On the forcing monophonic and forcing geodetic numbers of a graph, Indonesian Journal of Combinatorics, $4(2),(2020), 114-125$.
J. John and V. R. Sunil Kumar, The open detour number of a graph, Discrete Mathematics, Algorithms and Applications, 13(1),(2021),2050088(12 pages)
K.Krishna Kumari, S.Kavitha and D.Nidha, The open detour monophonic number of a graph.(communicated)
K.Krishna Kumari, S.Kavitha and D.Nidha, The open detour monophonic number of join,corona product and cluster product of graphs.(communicated)
A. P. Santhakumaran and P. Titus, Monophonic Distance in Graphs, Discrete Mathematics, Algorithms and Appli= cations, $3(2),(2011), 159-169$.
P. Titus, K. Ganesamoorthy and P. Balakrishnan. The Detour Monophonic Number of a Graph, J. Combin. Math. Combin. Comput., 84(2013), 179-188.
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