On the existence and the enumeration of bipartite regular representations of Cayley graphs over abelian groups

2020 ◽  
Vol 95 (4) ◽  
pp. 677-701 ◽  
Author(s):  
Jia‐Li Du ◽  
Yan‐Quan Feng ◽  
Pablo Spiga
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs ◽  
Regular Representations

Some properties of subgroup complementary addition Cayley graphs on abelian groups

2021 ◽  
Author(s):  
Naveen Palanivel ◽  
Chithra A. Velu
Keyword(s):  
Cayley Graph ◽  
Abelian Groups ◽  
Cayley Graphs ◽  
Graph Invariants

In this paper, we introduce subgroup complementary addition Cayley graph [Formula: see text] and compute its graph invariants. Also, we prove that [Formula: see text] if and only if [Formula: see text] for all [Formula: see text] where [Formula: see text].

Graphical Regular Representations of Non-Abelian Groups, II

1972 ◽  
Vol 24 (6) ◽  
pp. 1009-1018 ◽  
Author(s):  
Lewis A. Nowitz ◽  
Mark E. Watkins
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Regular Representation ◽  
Affirmative Answer ◽  
Roman Numeral ◽  
Regular Representations ◽  
Graphical Regular Representation ◽  
Bold Face

The present paper is a sequel to the previous paper bearing the same title by the same authors [3] and which will be hereafter designated by the bold-face Roman numeral I. Further results are obtained in determining whether a given finite non-abelian group G has a graphical regular representation. In particular, an affirmative answer will be given if (|G|, 6) = 1.Inasmuch as much of the machinery of I will be required in the proofs to be presented and a perusal of I is strongly recommended to set the stage and provide motivation for this paper, an independent and redundant introduction will be omitted in the interest of economy.

scholarly journals Cubic bi-Cayley graphs over abelian groups

2014 ◽  
Vol 36 ◽  
pp. 679-693 ◽  
Author(s):  
Jin-Xin Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs

One-matching bi-Cayley graphs over abelian groups

2009 ◽  
Vol 30 (2) ◽  
pp. 602-616 ◽  
Author(s):  
István Kovács ◽  
Aleksander Malnič ◽  
Dragan Marušič ◽  
Štefko Miklavič
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs
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