Geodesic
On integral sum graphs with a saturated vertex
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 669-674 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $G$. \endgraf 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 {\it saturated} if it is adjacent to every other vertex of $G$.) Some direct corollaries are also presented.
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 $G$. \endgraf 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 {\it saturated} if it is adjacent to every other vertex of $G$.) Some direct corollaries are also presented.
Classification : 05C15, 05C78
Keywords: integral sum graph; saturated vertex; edge-chromatic number 
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     author = {Chen, Zhibo},
     title = {On integral sum graphs with a saturated vertex},
     journal = {Czechoslovak Mathematical Journal},
     pages = {669--674},
     year = {2010},
     volume = {60},
     number = {3},
     mrnumber = {2672408},
     zbl = {1224.05439},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a5/}
}
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Chen, Zhibo. On integral sum graphs with a saturated vertex. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 669-674. http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a5/