Due to the widespread use of digital images of real-world objects as mathematical models, this research examines the freezing sets invariant-base properties of digital images. In contrast to earlier studies that only covered a discrete or limited collection of points, fixed points of digitally continuous functions are approved to deal with a variety of characteristics of digital images.

A theorem of Pompeiu states that the distances from the vertices of an equilateral triangle to an arbitrary point in its plane can serve as the side lengths of a triangle. A similar theorem holds for the medians of any triangle. Generalizations to higher dimensions of Pompeiu's theorem are established by M. Fiedler in 1977 and by Gh. Al-Afifi et al in a forthcoming paper. This paper is concerned with similar possible higher dimensional theorems for the medians. (2010): 51M04, 51M16, 51M15, 51M25, 51M20. Mathematics subject classification

Let be a completely regular Hausdorff space and let ( ) be the ring of all continuous real valued functions defined on . In this paper, the line graph for the zero-divisor graph of ( ) is studied. It is shown that this graph is connected with diameter less than or equal to 3 and girth 3. It is shown that this graph is always triangulated and hypertriangulated. It is characterized when the graph is complemented. It is proved that the radius of this graph is 2 if and only if has isolated points; otherwise, the radius is 3. Bounds for the dominating number and clique number are also found in terms of the density number of .

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