m-Bonacci graceful labeling
03 Feb 2021-AKCE International Journal of Graphs and Combinatorics (Taylor & Francis)-Vol. 18, Iss: 1, pp 7-15
TL;DR: A graph G on n edges is m-bonacci graceful if the vertices can be labeled with distinct integers from the set { 0, 1, 2, …, Z n, m...
About: This article is published in AKCE International Journal of Graphs and Combinatorics.The article was published on 2021-02-03 and is currently open access. It has received 1 citations till now. The article focuses on the topics: Graceful labeling & Graph (abstract data type).
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Book•
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14 Aug 2008
TL;DR: This book provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal, and is suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science.
Abstract: Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics computer science, combinatorial optimization, and operations research in particular but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance. The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided to help the reader master the techniques and reinforce their grasp of the material. A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters. Visit the graph theory book blog at: http://blogs.springer.com/bondyandmurty/.
3,296 citations
Journal Article•
TL;DR: In this survey I have collected everything I could find on graph labelings techniques that have appeared in journals that are not widely available.
Abstract: 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.
2,367 citations
01 Jan 1972
TL;DR: In this paper, the problem of numbering a graph is to assign integers to the nodes so as to achieve a given goal, i.e., to assign integer values to each node in a graph so that the number of nodes in the graph can be expressed as a function of the relationship between the nodes and the target nodes.
Abstract: Publisher Summary This chapter explains the way of numbering a graph. The problem of numbering a graph is to assign integers to the nodes so as to achieve G(Г). The principal questions which arise in the theory of numbering the nodes of graphs revolve around the relationship between G(Г) and e, for example, identifying classes of graphs for which G(Г)= e and other classes for which G(Г)
297 citations
TL;DR: A new type of labeling of a graph G with p vertices and q edges is introduced called an edge odd graceful labeling if there is a bijection f from the edges of the graph to the se...
24 citations
Posted Content•
TL;DR: With this algorithm, it is shown that every tree with at most 35 vertices allows a graceful labelling, hence it is verified that the graceful tree conjecture is correct for trees with at least 35 Vertices.
Abstract: Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every tree with at most 35 vertices allows a graceful labelling, hence we verify that the graceful tree conjecture is correct for trees with at most 35 vertices.
21 citations