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...

Full description

Bibliographic Details
Main Authors:	Gary Chartrand, Farrokh Saba, John K. Cooper, Frank Harary, Curtiss E. Wall
Format:	Article
Language:	English
Published:	Hindawi Limited 1982-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	cutpoins bridges cubic graphs quartic graphs.
Online Access:	http://dx.doi.org/10.1155/S0161171282000052

id	doaj-5134bc33beb14533a2f7752f23228886
record_format	Article
spelling	doaj-5134bc33beb14533a2f7752f232288862020-11-24T22:57:06ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-0151414810.1155/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	0161-1712 1687-0425
publishDate	1982-01-01
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
work_keys_str_mv	AT garychartrand smallestcubicandquarticgraphswithagivennumberofcutpointsandbridges AT farrokhsaba smallestcubicandquarticgraphswithagivennumberofcutpointsandbridges AT johnkcooper smallestcubicandquarticgraphswithagivennumberofcutpointsandbridges AT frankharary smallestcubicandquarticgraphswithagivennumberofcutpointsandbridges AT curtissewall smallestcubicandquarticgraphswithagivennumberofcutpointsandbridges
_version_	1725652005890818048

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

Similar Items