In this paper, a new concept -size edge resolving set for a connected graph in the context of resolvability of graphs is defined. Some properties and realizable results on -size edge resolvability of graphs are studied. The existence of this new parameter in different graphs is investigated, and the -size edge metric dimension of path, cycle, and complete bipartite graph is computed. It is shown that these families have unbounded -size edge metric dimension. Furthermore, the k-size edge metric dimension of the graphs P_m □ P_n, P_m □ C_n for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant -size edge metric dimension.

中文翻译：

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图的-Size边缘度量维

在本文中，定义了一个新概念-在图的可解性上下文中为连接的图的大小边缘解析集。某些属性和变现的结果-图的大小边缘可分解性进行了研究。在不同的图形这个新参数的存在进行了研究，并且-路径，循环，和完全二部图的大小边缘度量尺寸被计算。结果表明，这些家庭有无限的-尺寸边缘度量维度。此外，ķ的曲线图-size边缘度量尺寸P_米 □  P _Ñ，P_米 □  Ç _Ñ为米，Ñ ≥3和广义Petersen图被确定。结果表明，图的这些家庭都有固定-大小边缘度量维度。