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A (p, g) -graph G is Euclidean if there exists a bijection f: V → 1, 2, …, p such that for any induced C 3 -subgraph v 1, v 2, v 3 in G with f (v 1) f (v 3). The Euclidean Deficiency of a graph G is the smallest integer k such that G ∪ N k is Euclidean. We study the Euclidean Deficiency of one-point union and one-edge union of complete graphs.
Gao et al. (Sun,) studied this question.