摘要:

AbstractWe discuss the problem of finding smallest graphs of given girthgand valencyv((v, g)‐cages). All known (v, g)‐cages are given. Different variations of the cage problem are also discus

ISSN:0364-9024    

DOI:10.1002/jgt.3190060103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractA setDof vertices in a graph is said to be a dominating set if every vertex not inDis adjacent to some vertex inD.The domination number β(G) of a graphGis the size of a smallest dominating set.Gis called domination balanced if its vertex set can be partitioned into β(G) subsets so that each subset is a smallest dominating set of the complementGofG.The purpose of this paper is to characterize these graph

ISSN:0364-9024    

DOI:10.1002/jgt.3190060104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractThe object of this paper is to show that 4‐connected planar graphs are uniquely determined from their collection of edge‐deleted subgra

ISSN:0364-9024    

DOI:10.1002/jgt.3190060105

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractIfnis divisible by at least three distinct primes, the dihedral groupDncan be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation ofDnfor several families ofnand for all admissiblen<120. All these graphs are trivalent, bipartite, Hamiltonian, of girth 6, and are regular representations of their groups. For eachn, the isomorphism classes are determined and the graphs are described by a simple code.

ISSN:0364-9024    

DOI:10.1002/jgt.3190060106

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractLetGbe a graph with a known triangular embedding in a surfaceS, and considerG(m), the composition ofGwith an independant set of orderm.The purpose of this paper is to construct a triangular embedding ofG(m)into a surfaceby using a covering triangulation with folds. We make the construction for three cases. One of them is used for proving thatG(m)can be triangularly embedded into a surfaceifGis an Eulerian graph which can be triangularly embedded into a surfaceSwith the same orientability characteristic as.

ISSN:0364-9024    

DOI:10.1002/jgt.3190060107

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractLetG[H] denote the composition of the graphsGandH.IfGcan be decomposed into one‐factors and two‐factors,Hcan be decomposed into one‐factors, andHis not the empty graph on an odd number of vertices, thenG[H] can be decomposed into one‐

ISSN:0364-9024    

DOI:10.1002/jgt.3190060108

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractFor every positive integerc, we construct a pairGc,Hcof infinite, nonisomorphic graphs both having exactlyccomponents such thatGcandHcare hypomorphic, i.e.,GcandHchave the same families of vertex‐deleted subgraphs. This solves a problem of Bondy and Hemminger. Furthermore, the pairG1,H1is an example for a pair of non‐isomorphic, hypomorphic, connected graphs also having connected complements—a property not shared by any of the previously known counterexamples to the reconstruction conjecture for infinite g

ISSN:0364-9024    

DOI:10.1002/jgt.3190060109

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractA strongly harmonious labeling is the nonmodular version of a harmonious labeling. The windmill graphK(t)nis the graph consisting oftcopies of the complete graphKnwith a vertex in common. It is shown that, fort≥ 1,K(t)nis strongly harmonious and so harmonious by drawing on partitions already available from the construction of cyclic neofields. Other irregular windmill graphs can be shown to be strongly harmonious in a similar wa

ISSN:0364-9024    

DOI:10.1002/jgt.3190060110

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

摘要:

AbstractAs counterexamples to a conjecture of Randić, pairs of nonisomorphic trees with the same collections of distance degree sequences are presented

ISSN:0364-9024    

DOI:10.1002/jgt.3190060111

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY

ISSN:0364-9024    

DOI:10.1002/jgt.3190060112

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1982

数据来源: WILEY