A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

/pdf/a-dynamic-survey-of-graph-labeling-198znmwxtq.pdf

A Dynamic Survey of Graph Labeling

Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

/pdf/graph-coloring-problems-4v7vijos3s.pdf

Graph Coloring Problems

The processes underlying lignification, which for many years have been the near-exclusive purview of chemists and biochemists, have more recently been approached using both classical forward genetic screens and targeted reverse genetic approaches such as antisense suppression, RNAi, and characterization of insertional mutants. In this review, we provide an overview of the current understanding of lignin biosynthesis and structure, with emphasis on mutant and transgenic plants that have contributed to this knowledge. We also discuss ongoing work aimed at elucidating the relationship between lignin structure and function in vivo, as well as the phenotypic consequences arising from genetic manipulation of the lignin biosynthetic pathway.

The Genetics of Lignin Biosynthesis: Connecting Genotype to Phenotype

In mammals, cadmium is widely considered as a non-genotoxic carcinogen acting through a methylation-dependent epigenetic mechanism. Here, the effects of Cd treatment on the DNA methylation patten are examined together with its effect on chromatin reconfiguration in Posidonia oceanica. DNA methylation level and pattern were analysed in actively growing organs, under short- (6 h) and long- (2 d or 4 d) term and low (10 mM) and high (50 mM) doses of Cd, through a Methylation-Sensitive Amplification Polymorphism technique and an immunocytological approach, respectively. The expression of one member of the CHROMOMETHYLASE (CMT) family, a DNA methyltransferase, was also assessed by qRT-PCR. Nuclear chromatin ultrastructure was investigated by transmission electron microscopy. Cd treatment induced a DNA hypermethylation, as well as an up-regulation of CMT, indicating that de novo methylation did indeed occur. Moreover, a high dose of Cd led to a progressive heterochromatinization of interphase nuclei and apoptotic figures were also observed after long-term treatment. The data demonstrate that Cd perturbs the DNA methylation status through the involvement of a specific methyltransferase. Such changes are linked to nuclear chromatin reconfiguration likely to establish a new balance of expressed/repressed chromatin. Overall, the data show an epigenetic basis to the mechanism underlying Cd toxicity in plants.

/pdf/in-posidonia-oceanica-cadmium-induces-changes-in-dna-3cu7uj83mr.pdf

In Posidonia oceanica cadmium induces changes in DNA methylation and chromatin patterning

Families of Phenolic Compounds and Means of Classification.- Chemical Properties of Phenolic Compounds.- Biosynthesis of Phenolic Compounds.- Isolation and Identification of Phenolic Compounds.- Analysis of Phenolic Compounds with Mass Spectrometry.- The Role of Phenols in Plant Defense.- Phenolic Compounds and their Effects on Human Health.

Phenolic compound biochemistry

Brown-midrib (bm) mutants of maize have modified lignin of reddish-brown colour. Although four independent bm loci are known, only one of the mutant genes has been previously identified. We report here that maize bm1, one of the less characterised mutants, shows severely reduced CAD activity in lignified tissues, resulting in the production of a modified lignin. Both the total lignin content and the structure of the polymer are altered by the mutation. We further describe the isolation and characterisation of the maize CAD cDNA and mapping of the CAD gene. CAD maps very closely to the known location of bm1 and co-segregates with the bm1 locus in two independent recombinant inbred populations. These data strongly support the premise that maize bm1 directly affects expression of the CAD gene.

https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365-313X.1998.00153.x

Brown-midrib maize (bm1)--a mutation affecting the cinnamyl alcohol dehydrogenase gene.

Summary The harmonious chromatic number of a graph is the least number of colours in a vertex colouring such that each pair of colours appears on at most one edge The achromatic number of a graph is the greatest number of colours in a vertex colouring such that each pair of colours appears on at least one edge This paper is a survey of what is known about these two parameters, in particular we look at upper and lower bounds, special classes of graphs and complexity issues Introduction A short survey of harmonious colourings was given by Wilson [80] in 1990 Since then a number of new results have appeared, and the close relationship between harmonious chromatic number and achromatic number has been observed The purpose of this new survey is to outline what is known about these parameters, and suggest some open problems A more detailed summary of results on the achromatic number, with a rather different emphasis, can be found in the forthcoming survey by Hughes and MacGillivray [51] We begin with the definitions of the two parameters Definitions A harmonious colouring of a graph G is a proper vertex colouring of G such that, for any pair of colours, there is at most one edge of G whose endpoints are coloured with this pair of colours The harmonious chromatic number of G, denoted h(G), is the least number of colours in a harmonious colouring of G

The harmonious chromatic number and the achromatic number

Let G be a simple graph. The achromatic number ψ(G) is the largest number of colors possible in a proper vertex coloring of G in which each pair of colors is adjacent somewhere in G. For any positive integer m, let q(m) be the largest integer k such that ≤ m. We show that the problem of determining the achromatic number of a tree is NP-hard. We further prove that almost all trees T satisfy ψ (T) = q(m), where m is the number of edges in T. Lastly, for fixed d and ϵ > 0, we show that there is an integer N0 = N0(d, ϵ) such that if G is a graph with maximum degree at most d, and m ≥ N0 edges, then (1 - ϵ)q(m) ≤ ψ (G) ≤ q(m). © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 129–136, 1997

Some results on the achromatic number

Fragmentability of Graphs

We present an improved upper bound on the harmonious chromatic number of an arbitrary graph. We also consider „fragmentable” classes of graphs (an example is the class of planar graphs) that are, roughly speaking, graphs that can be decomposed into bounded-sized components by removing a small proportion of the vertices. We show that for such graphs of bounded degree the harmonious chromatic number is close to the lower bound (2m)1/2, where m is the number of edges.

New upper bounds on harmonious colorings

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Keith Edwards

Author Tools

Chat about Author