Abstract
The purpose of this paper is the study of simple graphs that are generalized Cayley graphs over LA-polygroups GCLAP − graphs . In this regard, we construct two new extensions for building LA-polygroups. Then, we define Cayley graph over LA-group and GCLAP-graph. Further, we investigate a few properties of them to show that each simple graph of order three, four, and five (except cycle graph of order five which may or may not be a GCLAP-graph) is a GCLAP-graph and then we prove this result.
Highlights
E idea of Cayley graph was introduced by Cayley [2] in 1878
In the books [10,11,12,13], we can see the applications of hyperstructures in lattices, cryptography, graph, automata, probability, geometry, and hypergraphs
E theory of left almost structures was first defined by Kazim and Naseeruddin [19] in 1972
Summary
E idea of Cayley graph was introduced by Cayley [2] in 1878. Cayley graph has been widely studied in both directed and undirected forms. En, we define the generalized Cayley graph over LA-polygroup GCLAP(L; C) which is the simple graph having vertex set L If we have an LA-polygroup L and a connection set C such that GCLAP(L; C) Λ, the graph Λ is known as a GCLAP-graph.
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