On the beta-number of linear forests with an even number of components

Peer review under responsibility of Kalasalingam University.

Figures & data

Table 1 Some vertex labelings of $F_1$, $F_2$, $F_3$ and $F$.

$m$	$n$	$F_1$	$F_2$	$F_3$	$F$
3	4	$(0,2,1)$	$(1,2,0)$	$\left(0\right)$	$(1,6,2),(4,5,3,0)$
3	5	$(0,2,1)$	$(3,0,2,1)$	$\left(0\right)$	$(1,7,2),(6,3,5,4,0)$
3	6	$(0,2,1)$	$(4,0,3,1,2)$	$\left(0\right)$	$(1,8,2),(7,3,6,4,5,0)$
4	5	$(0,3,1,2)$	$(3,0,2,1)$	$\left(0\right)$	$(1,8,2,7),(6,3,5,4,0)$
4	6	$(0,3,1,2)$	$(4,0,3,1,2)$	$\left(0\right)$	$(1,9,2,8),(7,3,6,4,5,0)$
4	7	$(0,3,1,2)$	$(4,1,5,0,2,3)$	$\left(0\right)$	$(1,10,2,9),(7,4,8,3,5,6,0)$