Sequentially additive graphs

TL;DR: This paper gives some new constructions of perfect splitter sets, as well as some nonexistence results on them, and obtain some new results on optimal conflict-avoiding codes.

TL;DR: Many of the variations of graceful and harmonious labeling methods that have been introduced are surveyed and much of what is known about each kind is summarized.

TL;DR: The super gracefulness of complete graph, the disjoint union of certain star graphs, the complete tripartite graphs K ( 1, 1, n ) , and certain families of trees is studied and it is conjecture that all trees are super graceful.

TL;DR: In this paper, the authors considered several types of additive bases and showed that a connected graph with n edges is called harmonious if it is possible to label the vertices with distinct numbers in such a way that the edge sums are also distinct (modulo n).

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: 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.