International Journal of Mathematics and Mathematical Sciences
For positive integers b and c, with c even, satisfying the inequalities b+1≤c≤2b, 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 such smallest quartic graphs are determined.
Original Publication Citation
Chartrand, G., Saba, F., Cooper, J. K., Harary, F., & Wall, C. E. (1982). Smallest cubic and quartic graphs with a given number of cutpoints and bridges. International Journal of Mathematics and Mathematical Sciences, 5(1), 41-48. doi:10.1155/s0161171282000052
Chartrand, Gary; Saba, Farrokh; Cooper, John K. Jr.; Harary, Frank; and Wall, Curtiss E., "Smallest Cubic and Quartic Graphs With a Given Number of Cutpoints and Bridges" (1982). Mathematics & Statistics Faculty Publications. 76.
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.