Determining The Number of Connected Vertex Labeled Graphs of Order Seven without Loops by Observing The Patterns of Formula for Lower Order Graphs with Similar Property

Muslim Ansori (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandar Lampung, 35145, Indonesia)
Wamiliana (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandar Lampung, 35145, Indonesia)
Fadila Cahya Puri (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandar Lampung, 35145, Indonesia)

Science and Technology Indonesia
Vol. 6 No. 4 (2021): October

Given n vertices and m edges, m ≥ 1, and for every vertex is given a label, there are lots of graphs that can be obtained. The graphs obtained may be simple or not simple, connected or disconnected. A graph G(V,E) is called simple if G(V,E) not containing loops nor paralel edges. An edge which has the same end vertex is called a loop, and paralel edges are two or more edges which connect the same set of vertices. Let N(G7,m,t) as the number of connected vertex labeled graphs of order seven with m vertices and t (t is the number edges that connect different pair of vertices). The result shows that N(G7,m,t) = ct C (m−1) t−1, with c6=6727, c7=30160 , c8=30765, c9=21000, c10=28364, c11=26880, c12=26460, c13=20790, c14=10290, c15= 8022, c16=2940, c17=4417, c18=2835, c19=210, c20= 21, c21=1.