the financial support from the Slovenian Research Agency(research core funding No.P1-0222).
We prove that the Laplacian matrix of the total graph of a finite commutative ring with identity has integer eigenvalues and present a recursive formula for computing its eigenvalues and eigenvectors.We also prove tha...
Let U^(g)_(n)be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),…,T_(g))∈U^(g)_(n)be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in an anticlockwise direction)by identifying v_(i)with...