### Abstract

As introduced by F. Harary in 1994, a graph G is said to be an integral sum graph if its vertices can be given a labeling f with distinct integers so that for any two distinct vertices u and v of G, uv is an edge of G if and only if f(u)+f(v) = f(w) for some vertex w in G. We prove that every integral sum graph with a saturated vertex, except the complete graph K_{3}, has edge-chromatic number equal to its maximum degree. (A vertex of a graph G is said to be saturated if it is adjacent to every other vertex of G.) Some direct corollaries are also presented.

Original language | English (US) |
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Pages (from-to) | 669-674 |

Number of pages | 6 |

Journal | Czechoslovak Mathematical Journal |

Volume | 60 |

Issue number | 3 |

DOIs | |

State | Published - Aug 10 2010 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Chen, Z. (2010). On integral sum graphs with a saturated vertex.

*Czechoslovak Mathematical Journal*,*60*(3), 669-674. https://doi.org/10.1007/s10587-010-0061-z