Total Energy of Cycle and Some Cycle Related Graphs

In this article we write algorithms and MATLAB programs to find the total energy of Cycle and some Cycle related graphs. The concept of total matrix and total energy of a graph G is introduced by K.Palani&M.Lalithakumari in [9]. Let G=(V, E) be a (p, q) simple graph. Let V ( G ) = { ν i / i = 1,2, … p } and E ( G ) = { e i / i = 1,2, … q }. The total matrix T = T ( G ) of G is a square matrix of order p + q whose (i, j)-entry is defined as: T = ( t i j ) = { 1 if v i adjacent to v j i ≠ j 1 if e i adjacent to e j i ≠ j 1 e i incident with v j 0 otherwise The Total Energy of a graph is the sum of absolute value of the eigen values of its Total matrix T ( G ). For any (p, q) graph G, the total number of eigen value is p+q. Let λ 1 , λ 2 , λ 3 , … λ p + q be the eigen values of T. Then total energy of G is T E = ∑ i + 1 p + q | λ i | .