In this paper, we characterized the balanced bicliques of graphs resulting from the join and the corona of graphs. Furthermore, we established the balanced biclique polynomials of the resulting graphs using combinatorial approach.
This study introduces a new geodetic invariant, the path-induced geodetic number of a connected simple graph G. We investigate its properties and characterize the path-induced geodetic sets of some common graphs. Also, the path-induced geodetic numbers of these graphs are determined