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Incremental Distance and Diameter Sequences of a Graph: New Measures of Network Performance
February 1990 (vol. 39 no. 2)
pp. 230-237

Two new measures of network performance, namely, the incremental distance sequence and the incremental diameter sequence, are introduced for application in network topology design. These sequences can be defined for both vertex deletions and edge deletions. A complete characterization of the vertex-deleted incremental distance sequence is presented. Proof of this characterization is constructive in nature. A condition for the feasibility of an edge-deleted incremental distance sequence and a procedure for realizing such a sequence are given. Interrelationships between the elements of incremental distance sequences and incremental diameter sequences are studied. Using these results, it is shown that a graph that has a specified diameter and a specified maximum increase in diameters for deletions of vertex sets of given cardinalities can be designed.

[1] J. C. Bermond, J. Bond, M. Paoli, and C. Peyrat, "Graphs and interconnection networks: Diameter and vulnerability," inSurveys in Combinatorics, E. K. Lloyd, Ed., LMS Lecture Note Series 82, 1983, pp. 1-30.
[2] M. Imase, T. Soneoka, and K. Okada, "Connectivity of regular directed graphs with small diameters,"IEEE Trans. Comput., vol. 34, pp. 267-273, 1985.
[3] U. Schumacher, "An algorithm for construction of a k-connected graph with minimum number of edges and quasiminimal diameter,"Networks, vol. 14, pp. 63-74, 1984.
[4] V. Krishnamoorthy, K. Thulasiraman, and M. N. S. Swamy, "Minimum order graphs wth specified diameter, connectivity and regularity,"Networks, to be published.
[5] F. R. K. Chung and M. R. Garey, "Diameter bounds for altered graphs,"J. Graph Theory, vol. 8, pp. 511-534, 1984.
[6] C. Peyrat, "Diameter vulnerability of graphs,"Discrete Appl. Math., vol. 9, pp. 245-250, 1984.
[7] F. T. Boesch, F. Harary, and J. A. Kabell, "Graphs as models of communication network vulnerability: Connectivity and persistence,"Networks, vol. 11, pp. 57-63, 1981.
[8] S. M. Reddy, J. G. Kuhl, S. H. Hosseini, and H. Lee, "On digraphs with minimum diameter and maximum connectivity," inProc. 20th Annu. Allerton Conf. Commun., Contr., Comput., 1982, pp. 1018-1026.
[9] J. G. Kuhl, "Fault-diagnosis in computing networks," Ph.D. dissertation, Dep. Elec. Comput. Eng., Univ. Iowa, Iowa City, IA, Aug. 1980.
[10] A. Sengupta, A. Sen, and S. Bandyopadhyay, "On an optimally fault tolerant multiprocessor network architecture,"IEEE Trans. Comput., vol. C-36, pp. 619-623, May 1987.
[11] D. K. Pradhan, "Fault-tolerant multiprocessor link and bus network architecture,"IEEE Trans. Comput., vol. C-34, pp. 33-45, 1985.
[12] D. Dolev, J. Y. Halpern, B. Simons, and R. Strong, "A new look at fault-tolerant network routing,"Inform. Computat., vol. 72, no. 3, pp. 180-196, Mar. 1987.
[13] A. Broder, D. Dolev, M. Fischer; and B. Simons, "Efficient fault-tolerant routings in networks," inProc. 16th Annu. ACM Symp. Theory Comput., 1984, pp. 536-541.
[14] V. Krishnamoorthy, K. Thulasiraman, and M. N. S. Swamy, "Incremental distance and diameter sequences of a graph: New measures of fault-tolerance," Tech. Rep., Dep. Elec. Comput. Eng., Concordia Univ., Montreal, P.Q., Canada, 1988.
[15] F. Harary,Graph Theory. Reading, MA: Addison-Wesley, 1972.
[16] G. Exoo, "On a measure of communication network vulnerability,"Networks, vol. 12, pp. 405-409, 1982.

Index Terms:
measures of network performance; incremental distance sequence; incremental diameter sequence; network topology design; vertex deletions; edge deletions; graph; circuit reliability; fault tolerant computing; graph theory; multiprocessor interconnection networks.
V. Krishnamoorthy, K. Thulasiraman, M.N.S. Swam, "Incremental Distance and Diameter Sequences of a Graph: New Measures of Network Performance," IEEE Transactions on Computers, vol. 39, no. 2, pp. 230-237, Feb. 1990, doi:10.1109/12.45208
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