Discussiones Mathematicae Graph Theory 27(2) (2007)
251-268
DOI: https://doi.org/10.7151/dmgt.1359
FURTHER RESULTS ON SEQUENTIALLY ADDITIVE GRAPHS
Suresh Manjanath Hegde Department of mathematical and Computational sciences |
Mirka Miller School of Electrical Engineering and Computer Science |
Abstract
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.
Keywords: simply (k-)sequentially additive labelings (graphs), segregated labelings.
2000 Mathematics Subject Classification: 05C78.
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Received 4 January 2006
Revised 5 February 2007
Accepted 5 February 2007
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