This paper (falling within the purview of Physics Education Research in particular, and Science Education Research in general) deals with a very significant issue related to labeling of the physical quantities along the axes of coordinates in graphing. It has been discovered that the traditional norms of specification of physical quantities along the axes in graph drawing are ambiguous. Such norms of specification totally ignore the inherent nature of a physical quantity. Furthermore, as a result of such a specification, each coordinate of a point lying on the graph assumes a numerical value along with a unit tagged with it, thereby violating the most fundamental concept of Cartesian coordinate geometry according to which the coordinates of a point in two-dimensional real space should be an ordered pair of real numbers. To get rid of such an ambiguity, an unambiguous procedure of specifying the physical quantities along the axes of coordinates in graph drawing has been finally proposed. The issue raised in the paper along with the relevant solution offered are both original and novel, never considered by any one earlier and hence the present scheme could not be placed into context to other existing works on the same issue. However, the present work has been compared with two other earlier works reported by the author in relation to graphing to judge its novelty and originality.