The forcing vertex detour monophonic number of a graph

Peer review under responsibility of Kalasalingam University.

Research supported by DST Project No. SR/S4/MS: 570/09.

Figures & data

Fig. 2.1 The graph in Example 2.2.

Table 2.1 The forcing vertex detour monophonic numbers of the graph given in Fig. 2.1.

Vertex	Minimum		Minimum forcing
	-detour		-detour
	monophonic sets		monophonic sets
		2		1
		3		1
		2		0
		2	,	1
		2		1
		2		0

Fig. 2.2 A graph with .

Fig. 2.3 A graph with vertex detour monophonic vertices.

Fig. 2.4 A graph with and .

Fig. 2.5 A graph with and .

Table 3.1 The upper forcing vertex detour monophonic numbers of the graph given in Fig. 2.1.

Vertex	-sets		-forcing subsets
		2		1	2
		3		1	2
		2		0	0
		2	,	1	1
		2		1	1
		2		0	0

Fig. 3.1 The graph in Case 1 of Theorem 3.7 with and .

Fig. 3.2 The graph in Case 2 of Theorem 3.7 with and .

Fig. 3.3 The graph in Case 3 of Theorem 3.7 with and .