Edge Detour Monophonic Number of a Graph

A. P. Santhakumaran, P. Titus, K. Ganesamoorthy, P. Balakrishnan

Resumen


For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G) .We determine bounds for it and characterize graphs which realize these bounds. Also, certain general properties satisfied by an edge detour monophonic set are studied. It is shown that for positive integers a, b and c with 2 < a < b < c, there exists a connected graph G such that m(G) = a, m!(G) = b and edm(G) = c,where m(G) is the monophonic number and m! (G) is the edge monophonic number of G. Also, for any integers a and b with 2 < a < b, there exists a connected graph G such that dm(G) = a and edm(G)= b,where dm(G) is the detour monophonic number of a graph G.

Palabras clave


Monophonic number ; Edge monophonic number ; Detour monophonic number ; Edge detour monophonic number.

Texto completo:

PDF

Referencias


F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, Redwood City, CA, (1990).

G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks, 39 (1), pp. 1-6, (2002).

W. Hale, Frequency Assignment; Theory and Applications, Proc. IEEE, 68, pp. 1497-1514, (1980).

F. Harary, Graph Theory, Addison-Wesley, (1969).

F. Harary, E. Loukakis, and C. Tsouros, The Geodetic Number of a Graph, Math. Comput. Modeling 17 (11), pp. 87-95, (1993).

T. Mansour and M. Schork, Wiener, hyper-Wiener detour and hyper detour indices of bridge and chain graphs, J. Math. Chem., 47, pp. 72-98, (2010).

A.P. Santhakumaran, P. Titus and P. Balakrishnan, Some Realisation Results on Edge Monophonic Number of a Graph, communicated.

A.P. Santhakumaran, P. Titus and K. Ganesamoorthy, On the Monophonic Number of a Graph, communicated.

P. Titus, K. Ganesamoorthy and P. Balakrishnan, The Detour Monophonic Number of a Graph, J. Combin. Math. Combin. Comput., 84, pp. 179-188, (2013).

P. Titus and K. Ganesamoorthy, On the Detour Monophonic Number of a Graph, Ars Combinatoria, to appear.




DOI: http://dx.doi.org/10.4067/S0716-09172013000200007

Enlaces refback

  • No hay ningún enlace refback.