SPECTRA OF PRINCIPAL GRAPHS

INTEGER-MAGIC SPECTRA OF CYCLE RELATED GRAPHS

For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...

Principal Component Analysis of Spectra

This paper discusses principal component analysis (PCA) of integral transforms (spectra and autocovariance functions) of time-domain signals. It is illustrated using acoustic emissions from mechanical equipment. It was found that acoustic signals from different stages of operation appeared as distinct clusters in the PCA analysis. The clusters moved when machinery faults were present and the mo...

Cycle Spectra of Graphs

This thesis contains several new results about cycle spectra of graphs. The cycle spectrum of a graph G is the set of lengths of cycles in G. We focus on conditions which imply a rich cycle spectrum. We show a lower bound for the size of the cycle spectrum of cubic Hamiltonian graphs that do not contain a fixed subdivision of a claw as an induced subgraph. Furthermore, we consider cycle spectra...

Spectra of expansion graphs

Replace certain edges of a directed graph by chains and consider the e ect on the spectrum of the graph. It is shown that the spectral radius decreases monotonically with the expansion and that, for a strongly connected graph that is not a single cycle, the spectral radius decreases strictly monotonically with the expansion. A limiting formula is given for the spectral radius of the expanded gr...

Spectra of graphs