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GM was concerned with the predictability of response on the network GM anticipated robots and other automated equipment attached to the network, and predictability of response to a problem was very important MAP was a token-passing protocol that provided relatively uniform access time to each device on the network In contrast, Ethernet s CSMA/CD protocol could not guarantee any worst case access time to the network, because the frequency of collisions and retries on the network depended on the loading of the network GM also liked the broadband, cable TV wiring specification of MAP With broadband, the wiring could handle many channels at once, allowing for networking, video, and other communications over common cable The broadband wiring also provided greater immunity to electrical noise, such as that from welders and other equipment in the factory Ethernet, or 802.

CHAP. 2]

The graph G1 cannot be eulerian because it has odd degree vertices. But the hamiltonian cycle shown in Figure 15.51 on page 314 verifies that it is hamiltonian. The graph G2 is neither eulerian nor hamiltonian. a. b. c. d. e. f. g. h. i. j. k. l. Disconnected, cyclic, and spanning. Disconnected, acyclic, and spanning. Disconnected, cyclic, and spanning. Disconnected, cyclic, and not spanning. Connected, acyclic, and spanning. Connected, acyclic, and spanning. Connected, cyclic, and spanning. Connected, acyclic, and not spanning. Disconnected, cyclic, and spanning. Connected, cyclic, and not spanning. Disconnected, acyclic, and not spanning. Connected, acyclic, and not spanning.

The Zener diode in the voltage-regulator circuit of Fig. 2-45 has a constant reverse breakdown voltage VZ 8:2 V, for 75 mA iZ 1 A. If RL 9 , size RS so that vL VZ is regulated to (maintained at) 8.2 V while Vb varies by 10 percent from its nominal value of 12 V.

The two graphs shown in Figure 15.52 on page 314 are not isomorphic because the one on the left has a 4-cycle containing two vertices of degree 2 and the one on the right does not. Yet, all five conditions of Theorem 15.4 on page 289 are satisfied.

3, was more successful with most customers, partly because it had a head start Also, the imagined problems of responsiveness with Ethernet generally did not occur in practice In addition, the wiring was less expensive and less complicated 78 The HTTP protocol is essentially a protocol providing for file transfer between the server and the client Therefore, the HTTP protocol is said to be stateless; ie, the server receives a request, and the server satisfies the request with a file transfer, regardless of what has happened before with this client This statelessness has been a challenge to those developing applications to be delivered over the web For instance, a banking application will need to keep track of the account number of the individual making inquiries, even though the individual makes repeated inquiries and updates using several different screens (web pages).

iS RS + iZ + Vb _ + LZ _ iL + RL _

15.8 15.9

Fig. 2-45 By Ohm s law iL Now an application of KVL gives RS Vb VZ iZ iL 1 vL V 8:2 0:911 A Z 9 RL RL

and we use (1) to size RS for maximum Zener current IZ at the largest value of Vb : RS 1:1 12 8:2 2:62 1 0:911

The adjacency matrix for the complete graph on n vertices is an n-by-n boolean matrix with false value at each entry on the diagonal and true value at every other entry. The incidence matrices Mn for the complete graphs on n vertices are as follows: Its has n rows and n(n 1)/2 columns (see Theorem 15.2 on page 286). If n = 2, it is the 2-by-1 matrix containing true in both entries. If n > 2, it is the matrix A concatenated horizontally with the matrix obtained from Mn 1 by placing one row of all false values on top of it. The four matrices are shown in Figure 15.53. a. b. c. d. e. f. a. b. c. d. e. f. The digraph is shown in Figure 15.54. Yes, this is a digraph: It has at least one one-way edge. No, the digraph is not strongly connected: There is no path from C to D. Yes, the digraph is weakly connected: Its embedded (undirected) graph is connected. No, the digraph is not acyclic: It contains the cycle AFEDA. Its adjacency matrix is shown in Figure 15.55 on page 315. The digraph G1 is shown in Figure 15.56 on page 315. Yes it is a digraph: Its adjacency matrix is not symmetric. No, this is not a simple digraph because it has a loop. Yes, this digraph is strongly connected. Yes, this digraph is weakly connected. No, the digraph is not acyclic: It contains the cycle ADB.