By Lowell W. Beineke, Robin J. Wilson

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**Sample text**

In the design of switching systems much attention is focused on the problems of storage and control. The interdependence of the con nection configuration and the control problem has on occasion been recognized explicitly (see [39] or [47]), and is of course known im plicitly to designers of switching systems, but there has not been enough comparative study of configurations in terms of their appropriate control algorithms. The configuration of a major network, in which the vertices repre sent exchanges (as in Fig.

We can represent this by joining up several graphs, each of which represents part of the connection. For example, if two small exchanges are linked together by junction lines, then the whole configuration is that shown in Fig. 10. Topologically, the set of junctions whose ends are in one-to-one correspondence is immaterial, and we can shrink the graph to that of Fig. 11. The latter represents equally well the trunking of an exchange with three ranks 28 K. W. CATTERMOLE of switches (designated A , B and C) with links between adjacent stages.

31). Fig. 31 50 K. W. 6 Ui the summation being taken over all pairs of permutations 7, 5, and the product being taken over all pairs of cycle lengths i, with appro priate values of d and m for each pair. Taking as an example T = A = S (4the symmetri cycle index is X + 6XiX2 + 3*2 + 8X1X3 + 6X4), 1 it is readily found that the cycle index of S4 x £4 is §75(x j6 + 12x®X2 + 36X1X2 + 51x | + I6X1X3 + 64xiX® + 96x1X3X3X6 + 48x2X6 + 15x4 + 96x4X12), and the number of equivalence classes 2,. . , 2) = 317.

### Applications of graph theory by Lowell W. Beineke, Robin J. Wilson

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