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The Vertex Euclidean Properties of Graphs

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Abstract

A simple graph G = (V, E) is said to be vertex Euclidean if there exists a bijection f from V to {1, 2,…,∣V∣} such that f(u) + f(v) > f(w) for each C3 subgraph with vertex set {u, v, w}, where f(u) < f(v) < f(w). The vertex Euclidean deficiency of a graph G, denoted μvEuclid(G), is the smallest positive integer n such that G ∪ Nn is vertex Euclidean. In this paper, we introduce some methods for deriving the vertex Euclidean properties of some simple graphs.

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Authors and Affiliations

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, P. R. China

    Zhen Bin Gao & Meng Wang

  2. 1786 Plan Tree Drive, Upland, CA, 91784, USA

    Sin Min Lee

  3. Dept. of Math. Sci., SUNY Fredonia, Fredonia, New York, NY, 14063, USA

    Harris Kwong

  4. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, P. R. China

    Shu Juan Wang

Authors
  1. Zhen Bin Gao
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  2. Meng Wang
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  3. Sin Min Lee
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  4. Harris Kwong
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  5. Shu Juan Wang
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Correspondence to Harris Kwong.

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Gao, Z.B., Wang, M., Lee, S.M. et al. The Vertex Euclidean Properties of Graphs. Acta. Math. Sin.-English Ser. 38, 1185–1202 (2022). https://doi.org/10.1007/s10114-022-0378-1

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  • DOI: https://doi.org/10.1007/s10114-022-0378-1

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