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Full-Text Articles in Physical Sciences and Mathematics
Smallest Cubic And Quartic Graphs With A Given Number Of Cutpoints And Bridges, Gary Chartrand, Farrokh Saba, John K. Cooper Jr., Frank Harary, Curtiss E. Wall
Smallest Cubic And Quartic Graphs With A Given Number Of Cutpoints And Bridges, Gary Chartrand, Farrokh Saba, John K. Cooper Jr., Frank Harary, Curtiss E. Wall
Mathematics & Statistics Faculty Publications
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.