International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 1, Pages 41-48  Smallest cubic and
quartic graphs with a given number of cutpoints and bridges
Gary Chartrand,1 Farrokh Saba,1 John K. Cooper Jr.,2 Frank
Harary,3 and Curtiss E. Wall4  1Department of Mathematics,
Western Michigan University, Kalamazoo 49008, Michigan, USA
2Department of Mathematics, Eastern Michigan University,
Ypsilanti 48197, Michigan, USA 3Department of Mathematics,
University of Michigan, Ann Arbor 48104, Michigan, USA
4Department of Mathematics, Old Dominion University, Norfolk
23508, Virginia, USA  Received 6 April 1981    For positive
integers b and c, with c even, satisfying the inequalities
b+1c2b, the minimum order of a connected cubic graph with b
bridges and c cutpoints is computed. Furthermore, the structure
of all such smallest cubic graphs is determined. For each
positive integer c, the minimum order of a quartic graph with c
cutpoints is calculated. Moreover, the structure and number of
all