Abstract
A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we will examine cactus graphs where all the blocks are 3-cycles, i.e., triangular cactus graphs, of diameter 4. Our main focus is to prove that the corresponding edge ring of this family of graphs is not normal and satisfies Serre’s condition ( S 2 ) . We use a criterion due to Katthän for non-normal affine semigroup rings.
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