On the connected detour monophonic number of a graph
Citation
Titus, P. & Ganesamoorthy, K. (2021). On the connected detour monophonic number of a graph. TWMS Journal Of Applied And Engineering Mathematics, 11(4), 966-974.Abstract
For a connected graph G = (V, E) of order at least two, a connected detour monophonic set S of G is called a minimal connected detour monophonic set if no proper subset of S is a connected detour monophonic set of G. The upper connected detour monophonic number of G, denoted by dm+c (G), is defined as the maximum cardinality of a minimal connected detour monophonic set of G. We determine bounds for it and find the same for some special classes of graphs. For any three positive integers a, b and n with 6 ≤ a ≤ n ≤ b, there is a connected graph G with dmc(G) = a, dm+c (G) = b and a minimal connected detour monophonic set of cardinality n.
Source
TWMS Journal Of Applied And Engineering MathematicsVolume
11Issue
4URI
https://hdl.handle.net/11729/3246http://jaem.isikun.edu.tr/web/index.php/archive/113-vol11-no4/756
Collections
The following license files are associated with this item:
Related items
Showing items related by title, author, creator and subject.
-
The connected detour monophonic number of a graph
Titus, P.; Santhakumaran, A. P.; Ganesamoorthy, K. (Işık University Press, 2016)For a connected graph G = (V, E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A longest x − y monophonic path ... -
On the monophonic and monophonic domination polynomial of a graph
Sudhahar, Arul Paul; Jebi, W. (Işık University Press, 2024-01)A set S of vertices of a graph G is a monophonic set of G if each vertex u of G lies on an u − v monophonic path in G for some u, v ∈ S. M ⊆ V (G) is said to be a monophonic dominating set if it is both a monophonic set ... -
Minimal restrained monophonic sets in graphs
Santhakumaran, A. P.; Raghu T. Venkata; Ganesamoorthy, K. (Işık University Press, 2021)For a connected graph G = (V, E) of order at least two, a restrained monophonic set S of a graph G is a monophonic set such that either S = V or the subgraph induced by V −S has no isolated vertices. The minimum cardinality ...