Abstract: In any planar graph G there is a one to one correspondence between edges in G, its dual G∗. As the number of vertices and edges increase construction of G* is complicated, when graph G* is not required and only properties of G* is a need, determining properties of G* without actual construction of G* is comfortable. In this paper we determine the domination number of G*, G*, chromatic polynomial of G*, spanning tree of G*, number of spanning trees of G* from G. Determining the domination number of G*, G* using matrix representation is presented. MATLAB code for determining the same is also provided.
DOI: *As the DOI is a unique identifier, it is already available in the pdf version. **The DOI link will be activated in the first midst of January 2026.