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{...

Photonic crystal slabs are a versatile and important platform for molding the flow of light. In this thesis, we consider ways to control the emission of light from photonic crystal slab structures, specifically focusing on directional, asymmetric emission, and on emitting light with interesting topological features. First, we develop a general coupled-mode theory formalism to derive bounds on t...

THISESSAY PROPOSES A MODEL called information genetics (IG) to elaborate on the origin of information generating. The model builds on a broad information generating force that is both cause and effect. Part I of this essay postulates this information generating force as the result of the interaction and intermediation among four subforces: Query, command, statement, and term-term bond. These su...