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The Klee-Quaife problem is nding the minimum order (d; c; v) of the (d; c; v) graph, which is a c-vertex connected v-regular graph with diameter d. Many authors contributed nding (d; c; v) and they also enumerated and classi ed the graphs in several cases. This problem is naturally extended to the case of digraphs.
So we are interested in the extended Klee-Quaife problem.
In this paper, we deal with an equivalent problem, nding the maximum diameter of digraphs with given order, focused on 2-regular case. We show that the maximum diameter of strongly connected 2-regular digraphs with order n is n − 3, and classify the digraphs which have diameter n−3. All 15 nonisomorphic extremal digraphs are listed.
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참고문헌 (11)
참고문헌 신청
A. Knyazev / 1987 / Diameters of Pseudosymmetric Graphs (Russian) / Mat. Zametki 41 (6) : 829 ~ 843
B. Grunbaum / 1962 / Longest simple paths in polyhedral graphs / J. Lond. Math. Soc 37 : 152 ~ 160
B. Myers / 1980 / The minimum-order three-connected cubic graphs with specied diameters / IEEE Trans. Circuits Syst CAS-27 (8) : 698 ~ 709
D. Bhattacharya / 1985 / The minimum order of n-connected n-regular graphs with specied diameters / IEEE Trans. Circuits Syst CAS-32 (4) : 407 ~ 409
E. Engelhardt / 1989 / Minimum graphs of specied diam- eter, connectivity and valence. II / Discrete Math 78 (3) : 257 ~ 266
B. Grunbaum / 1962 / Longest simple paths in polyhedral graphs / J. Lond. Math. Soc 37 : 152 ~ 160
B. Myers / 1980 / The minimum-order three-connected cubic graphs with specied diameters / IEEE Trans. Circuits Syst CAS-27 (8) : 698 ~ 709
D. Bhattacharya / 1985 / The minimum order of n-connected n-regular graphs with specied diameters / IEEE Trans. Circuits Syst CAS-32 (4) : 407 ~ 409
E. Engelhardt / 1989 / Minimum graphs of specied diam- eter, connectivity and valence. II / Discrete Math 78 (3) : 257 ~ 266
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