The minimum number of vertices with girth 6 and degree set D={r, m}
نویسندگان
چکیده
A (D; g)-cage is a graph having the minimum number of vertices, with degree set D and girth g. Denote by f(D; g) the number of vertices in a (D; g)-cage. In this paper it is shown that f({r; m}; 6)¿ 2(rm−m+ 1) for any 26 r ¡m, and f({r; m}; 6) = 2(rm−m+ 1) if either (i) 26 r6 5 and r ¡m or (ii) m − 1 is a prime power and 26 r ¡m. Upon these results, it is conjectured that f({r; m}; 6) = 2(rm− m+ 1) for any r with 26 r ¡m. c © 2002 Elsevier B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 269 شماره
صفحات -
تاریخ انتشار 2003