On The automorphism groups of $us$-Cayley graphs
S.Morteza Mirafzal

TL;DR
This paper characterizes the automorphism groups of a class of Cayley graphs called $us$-Cayley graphs, showing they are semidirect products of the group with automorphisms preserving the generating set, and applies this to specific graph classes.
Contribution
It provides a complete description of automorphism groups for $us$-Cayley graphs, a new class defined by a unique summation property, and applies this to known graph families.
Findings
Automorphism group of $us$-Cayley graphs is $L(G) times A$.
Explicit automorphism groups for Möbius ladders.
Explicit automorphism groups for $k$-ary $n$-cubes.
Abstract
Let be a finite abelian group written additively with identity , and be an inverse closed generating subset of such that . We say that has the property \lq\lq{}\rq\rq{} (unique summation), whenever for every if there are such that , then we have . We say that a Cayley graph is a -, whenever is an abelian group and the generating subset has the property \lq\lq{}\rq\rq{}. In this paper, we show that if is a -, then , where is the left regular representation of and is the group of all automorphism groups of the group such that . Then, as some applications, we…
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Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Graph Labeling and Dimension Problems
