Smallest cubic and quartic graphs with a given number of cutpoints and bridges
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 q...
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19820101

Series:  International Journal of Mathematics and Mathematical Sciences 
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Online Access:  http://dx.doi.org/10.1155/S0161171282000052 
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doaj5134bc33beb14533a2f7752f2322888620201124T22:57:06ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences01611712168704251982010151414810.1155/S0161171282000052Smallest cubic and quartic graphs with a given number of cutpoints and bridgesGary Chartrand0Farrokh Saba1John K. Cooper2Frank Harary3Curtiss E. Wall4Department of Mathematics, Western Michigan University, Kalamazoo 49008, Michigan, USADepartment of Mathematics, Western Michigan University, Kalamazoo 49008, Michigan, USADepartment of Mathematics, Eastern Michigan University, Ypsilanti 48197, Michigan, USADepartment of Mathematics, University of Michigan, Ann Arbor 48104, Michigan, USADepartment of Mathematics, Old Dominion University, Norfolk 23508, Virginia, USAFor 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.http://dx.doi.org/10.1155/S0161171282000052cutpoinsbridgescubic graphsquartic graphs. 
collection 
DOAJ 
language 
English 
format 
Article 
sources 
DOAJ 
author 
Gary Chartrand Farrokh Saba John K. Cooper Frank Harary Curtiss E. Wall 
spellingShingle 
Gary Chartrand Farrokh Saba John K. Cooper Frank Harary Curtiss E. Wall Smallest cubic and quartic graphs with a given number of cutpoints and bridges International Journal of Mathematics and Mathematical Sciences cutpoins bridges cubic graphs quartic graphs. 
author_facet 
Gary Chartrand Farrokh Saba John K. Cooper Frank Harary Curtiss E. Wall 
author_sort 
Gary Chartrand 
title 
Smallest cubic and quartic graphs with a given number of cutpoints and bridges 
title_short 
Smallest cubic and quartic graphs with a given number of cutpoints and bridges 
title_full 
Smallest cubic and quartic graphs with a given number of cutpoints and bridges 
title_fullStr 
Smallest cubic and quartic graphs with a given number of cutpoints and bridges 
title_full_unstemmed 
Smallest cubic and quartic graphs with a given number of cutpoints and bridges 
title_sort 
smallest cubic and quartic graphs with a given number of cutpoints and bridges 
publisher 
Hindawi Limited 
series 
International Journal of Mathematics and Mathematical Sciences 
issn 
01611712 16870425 
publishDate 
19820101 
description 
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. 
topic 
cutpoins bridges cubic graphs quartic graphs. 
url 
http://dx.doi.org/10.1155/S0161171282000052 
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