In this paper, we study the relationship between eigenvalues and the existence of certain subgraphs in regular graphs. We give a condition on an appropriate eigenvalue that guarantees a lower bound for the matching number of a t-edge-connected d-regular graph, when t ≤ d − 2. This work extends some classical results of von Baebler and Berge and more recent work of Cioabă, Gregory, and Haemers. ...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

A SAS macro solution is presented for clustering of high dimensional low sample size (HDLLSS) data using a new algorithm based o p-values as similarity measure. The algorithm PPCLUST was developed by von Borries (2008) and implemented using SAS macro language with the macro autocall facility and window macro command for friendly interface. The SAS interface to JMP was used to run a SAS macro in...

We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr Z, with G a finite abelian group, by realizing them as groups generated by automata. This generalizes the work of Grigorchuk and Żuk on the lamplighter group. More generally we calculate the spectra of random walks on groups generated by Cayley machines of finite groups and calculate Kes...

A conceptual basin model of the instantaneous unit sediment graph was developed for sediment graph prediction from arid upland basins by routing mobilized sediments through a series of linear reservoirs. The sediment graphs generated by convolution of the instantaneous unit sediment graph compared reasonably well with the observed ones for four representative arid upland sub-basins in the Luni ...

the edge tenacity te(g) of a graph g is de ned as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...