We relate radio number of dublicated

cycle graph with the radio number number of cycle as follows.

n] is a

cycle graph then the middle graph of the

cycle graph M ([C.

The tadpole graph Tn k [13] is the graph obtained by joining a

cycle graph [C.

Loop analysis reveals the underlying pathway structure of the life

cycle graph.

3) "Decompose the life

cycle graph into branched loops in such a way that all transitions are incorporated at least once into some loop" (van Groenendael et al.

4)], who independently noted that the critical group of the

cycle graph on n vertices is Z/nZ, the cyclic group on n elements.

The basic step in loop analysis is to consider elasticities in the context of the underlying life history structure as exemplified by the life

cycle graph (Caswell 1989a).

2 Consider the

cycle graph G to the left in Figure 1, with k = 3 and two black edges.

Note that, apart from the path and

cycle graphs mentioned in Section 3, all graphs in this paper are directed, although we don't explicitly refer to them as directed graphs.

2] are

cycle graphs of lengths 3 and 4, respectively.

Users can view

cycle graphs, summary graphs, and machine status information in real time.