Arithmetic graphs

TL;DR: It is found that a strongly indexable graph has exactly one nontrivial component which is either a star or has a traingle in any strongly k-indexable graph the minimum point degree is at most 3.

TL;DR: In this article, the authors used matrices in order to find lower bounds for the number of non-isomorphic edge-magic labelings of certain types of graphs, and new applications of graph labelings are discussed.

TL;DR: The strength of the paper lays on the techniques used, since they are not only used in order to provide labelings of many different types of families of graphs, but they also show interesting relations among well studied types of labelings.

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.

TL;DR: It is shown that any tree admitting an α-valuation also admits a sequential labeling and hence is harmonious, and Constructions are given for new families of graceful and sequential graphs, generalizing some earlier results.

TL;DR: In this paper, the status of the 1963 conjecture of Ringel concerning the decomposition of K, into isomorphs of an arbitrary tree is explained and traced through its modification by Kotzig to the series of attacks intent on proving that trees are graceful.

TL;DR: In this paper an introductory study of k-sequential graphs is made and several variations on the problems of gracefully or sequentially numbering the elements of a graph are discussed.