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Full-Text Articles in Physical Sciences and Mathematics
Independence Polynomials And Extended Vertex Reduction, Jonathan Broom
Independence Polynomials And Extended Vertex Reduction, Jonathan Broom
Honors Theses
The independence polynomial of a graph is a polynomial whose coefficients number the independent sets of each size in that graph. This paper looks into methods of obtaining these polynomials for certain classes of graphs which prove too large to easily find the polynomial by traditional methods.
The Matrix Method Of Linear Dichroism, Kenna Collums
The Matrix Method Of Linear Dichroism, Kenna Collums
Honors Theses
This thesis discusses linear dichroism, and in particular the matrix method behind the spectroscopic technique. Linear dichroism uses the difference in the absorption of light that is parallel to the orientation axis and the absorption of light that is perpendicular to the orientation axis. From this process, the structure and function of molecules can be studied. The matrix method diagonalizes a Hamiltonian matrix with a unitary matrix. This Hamiltonian matrix is constructed from the transition energies, which are the diagonal elements, and coupling energies, which are off-diagonal elements.
The Tutte Polynomial Formula For The Class Of Twisted Wheel Graphs, Amanda Hall
The Tutte Polynomial Formula For The Class Of Twisted Wheel Graphs, Amanda Hall
Honors Theses
The 20th century work of William T. Tutte developed a graph polynomial that is modernly known as the Tutte polynomial. Graph polynomials, such as the Tutte polynomial, the chromatic polynomial, and the Jones polynomial, are at the heart of combinatorical and algebraic graph theory and can be used as tools with which to study graph invariants. Graph invariants, such as order, degree, size, and connectivity which are defined in Section 2, are graph properties preserved under all isomorphisms of a graph. Thus any graph polynomial is not dependent upon a particular labeling or drawing but presents relevant information about the …