This paper has an interest in the directions of algebra or combinatorics built or rooted on graphs. An algebraic axiom, namely, distributivity can be used to determine the number of edges in some algebraic expressions of graphs together with certain binary operations. In this approach, we have been able to estimate the number of edges in a resultant graph formed by two components simply by knowing the number of vertices in the respective graphs with the positions of non-adjacent vertices (if any), and consequently, the rank and the nullity are computed. The number of edges in a resultant graph formed by three components can be determined by using distributive property on knowing the number of vertices in each graphs and the number of edges of one of the components in addition to knowing the relative positions of non-adjacent vertices.
Volume 12 | 02-Special Issue