Given a graph G with p vertices, q edges and a positive integer k, a k-sequentially additive labeling of G is an assignment of distinct numbers k,k+1,k+2,...,k+p+q-1 to the p+q elements of G so that every edge uv of G receives the sum of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its elements is called a k-sequentially additive graph. In this paper, we give an upper bound for k with respect to which the given graph may possibly be k-sequentially additive using the independence number of the graph. Also, we prove a variety of results on k-sequentially additive graphs, including the number of isolated vertices to be added to a complete graph with four or more vertices to be simply sequentially additive and a construction of an infinite family of k-sequentially additive graphs from a given k-sequentially additive graph.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1359,
author = {Suresh Manjanath Hegde and Mirka Miller},
title = {Further results on sequentially additive graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {27},
year = {2007},
pages = {251-268},
zbl = {1139.05057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1359}
}
Suresh Manjanath Hegde; Mirka Miller. Further results on sequentially additive graphs. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 251-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1359/
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