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2. Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power orderEdward Dobson, 2010, original scientific article Abstract: We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫. Found in: ključnih besedah Summary of found: ...every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism... Keywords: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group Published: 15.10.2013; Views: 2856; Downloads: 74 Full text (0,00 KB) |
3. Group irregularity strength of connected graphsMarcin Anholcer, Sylwia Cichacz, Martin Milanič, 2013, original scientific article Found in: ključnih besedah Summary of found: ...irregularity strength, graph labelling, Abelian group, ... Keywords: irregularity strength, graph labelling, Abelian group Published: 15.10.2013; Views: 1043; Downloads: 60 Full text (0,00 KB) |
4. Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groupsŠtefko Miklavič, Primož Šparl, 2012, original scientific article Abstract: In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton cycle of ▫$\Gamma$▫. Similarly, ▫$\Gamma$▫ is weakly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton path of ▫$\Gamma$▫. Moreover, ▫$\Gamma$▫ is strongly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if for every such path $P$ there is a Hamilton path of ▫$\Gamma$▫ starting with ▫$P$▫. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2-HC-extendable and a complete classification of 3-HC-extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4-HP-extendable. Found in: ključnih besedah Summary of found: ...class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley... Keywords: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group Published: 15.10.2013; Views: 1420; Downloads: 85 Full text (0,00 KB) |
5. On overgroups of regular abelian p-groupsEdward Dobson, 2009, original scientific article Abstract: Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup ▫$P$▫ is abelian od rank ▫$t$▫. Weshow that if ▫$p > 2^{t-1}$▫, then ▫$G$▫ has a normal subgroup that is a direct product of ▫$t$▫ permutation groups of smaller degree that are either cyclic or doubly-transitive simple groups. As a consequence, we determine the full automorphism group of a Cayley diagraph of an abelian group with rank two such that the Sylow ▫$p$▫-subgroup of the full automorphism group is abelian. Found in: ključnih besedah Summary of found: ...Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup... Keywords: group theory, graph theory, Cayley graph, abelian group, regular group, p-group Published: 15.10.2013; Views: 1781; Downloads: 79 Full text (0,00 KB) |
6. On the split structure of lifted groupsAleksander Malnič, Rok Požar, 2016, original scientific article Found in: ključnih besedah Summary of found: ...algorithm, abelian cover, Cayley voltages, covering projection, graph, group... Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product Published: 15.10.2015; Views: 1205; Downloads: 67 Full text (0,00 KB) |
7. Cayley graphs on abelian groupsGabriel Verret, Edward Dobson, Pablo Spiga, 2015, original scientific article Found in: ključnih besedah Summary of found: ...Cayley graph, abelian group, automorphism, ... Keywords: Cayley graph, abelian group, automorphism Published: 03.04.2017; Views: 952; Downloads: 105 Full text (0,00 KB) |
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