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The pursuit to identify vertex-transitive non-Cayley graphs has been deliberate for some time now. In that vein, Alspach and Parsons [1] introduced metacirculant graphs. They are defined on two cyclic groups with adjacency resembling twisting that is typically used in defining semi-direct products of groups. In this sequel we generalise the construction to general groups and introduce a class of graphs we call meta-Cayley graphs. [ABSTRACT FROM PUBLISHER]

For any prime p, we consider p-ary linear codes obtained from the row span of incidence matrices of line graphs of triangular graphs and adjacency matrices of their line graphs. We determine parameters of the codes, their automorphism groups and exhibit permutation decoding sets (PD-sets) for partial permutation decoding. [ABSTRACT FROM AUTHOR]