In this paper, a generalization of a group-magic graph is introduced and studied. Let R be a commutative ring with unity 1. A graph G = (V,E) is called R-ring-magic if there exists a labeling f : E → R−{0} such that the induced vertex labelings f : V → R, defined by f(v) = Σf(u, v) where (u, v) ∈ E, and f : V → R, defined by f(v) = Πf(u, v) where (u, v) ∈ E, are constant maps. General algebraic...

24 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection 25 l : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum 26 of the labels on the vertices in the open neighborhood of v, is a constant. 27 In this paper, we show that hypercubes with dimension divisible by four 28 are not distance magic. We also provide some positive results by providing ...

In this paper, we are studying vertex-magic total labelings (VMTLs) of simple graphs. By now much is known about methods for constructing VMTLs for regular graphs. Here we are studying non-regular graphs. We show how to construct labelings for several families of non-regular graphs, including graphs formed as the disjoint union of two other graphs already possessing VMTLs. We focus on condition...

“Super-resolution” is the term used to denote the subset of imaging processing that tries to estimate a high-resolution image of a scene, given a set of low-resolution observations (Fig. 1). Colloquially, when superresolution researchers try to describe what they do to family, friends, and loved ones, we can use the example from the TV show CSI: whenever someone on CSI looks at low-resolution s...

Let G be a (p, q) graph and let f : V (G) → {1, 2, 3, · · · , p + q} be an injection. For each edge e = uv, let f∗(e) = (f(u)+f(v))/2 if f(u)+f(v) is even and f∗(e) = (f(u)+f(v)+1)/2 if f(u) + f(v) is odd. Then f is called a super mean labeling if f(V ) ∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, · · · , p+ q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we presen...

This paper considers the efficient bottom-up query evaluation for stratified databases. We investigate the applicability of magic-set method to stratified databases containing negative body literals and show that culprit cycles cause unstratification. Based on the analysis, we present a labeling algorithm to distinguish the context for constructing magic sets, which is simpler and more efficien...

Previous stochastic localization-based super-resolution techniques are largely limited by the labeling density and the fidelity to the morphology of specimen. We report on an optical super-resolution imaging scheme implementing joint tagging using multiple fluorescent blinking dyes associated with super-resolution optical fluctuation imaging (JT-SOFI), achieving ultra-high labeling density supe...

Let [n]∗ denote the set of integers {−n−1 2 , . . . , n−1 2 } if n is odd, and {−n 2 , . . . , n 2 } \ {0} if n is even. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) → [q]∗, such that the induced vertex labeling f ∗ given by f ∗(u) = ∑ uv E(G) f(uv) is a bijection f ∗ : V (G) → [p]∗. A graph is super edge-graceful if it has a super edge-graceful la...

In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertices. The result of a mutation may be a different labeling of the same graph or a labeling of a different graph. Mutation proves to be a remarkably fruitful process— for example we are able to genera...

CRISPR/dCas9-based labeling has allowed direct visualization of genomic regions in living cells. However, poor labeling efficiency and signal-to-background ratio have limited its application to visualize genome organization using super-resolution microscopy. We developed (Po)STAC (Polycistronic SunTAg modified CRISPR) by combining CRISPR/dCas9 with SunTag labeling and polycistronic vectors. (Po...