论文标题
图形的总和索引和差异索引
Sum index and difference index of graphs
论文作者
论文摘要
让$ g $是一个非空的简单图，带有顶点套装$ v（g）$和边缘集$ e（g）$。对于每个注入性顶点标签$ f：v（g）\ to \ mathbb {z} $，有两个诱导的边缘标签，即$ f^+：e（g）\ to \ mathbb {z} $由$ f^+（uv）= f^+（uv）= f（uv）= f（u）+f（v）+f（v）$ f^$ f^$ f^$ e（e（g）由$ f^ - （uv）= | f（u）-f（v）| $。总和索引和差异指数分别是$ f^+$和$ f^ - $的最小基数。我们在总和指数和差异指数上提供上限和下限，并确定各个图的总和指数和差异指数。我们还提供了一个有趣的猜想，该猜想与图形的总和索引有关。
Let $G$ be a nonempty simple graph with a vertex set $V(G)$ and an edge set $E(G)$. For every injective vertex labeling $f:V(G)\to\mathbb{Z}$, there are two induced edge labelings, namely $f^+:E(G)\to\mathbb{Z}$ defined by $f^+(uv)=f(u)+f(v)$, and $f^-:E(G)\to\mathbb{Z}$ defined by $f^-(uv)=|f(u)-f(v)|$. The sum index and the difference index are the minimum cardinalities of the ranges of $f^+$ and $f^-$, respectively. We provide upper and lower bounds on the sum index and difference index, and determine the sum index and difference index of various families of graphs. We also provide an interesting conjecture relating the sum index and the difference index of graphs.
