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Weak integer additive set-labeled graphs: a creative review. (English) Zbl 1328.05164

Graph labeling problems started with the introduction of the concept of number valuation of graphs. Motivated from various problems related to social interaction and social networks and analogous to the number valuation of graphs, the notion of set-valuations of graphs was also introduced. In addition, an integer additive set-indexer (IASI) is defined. The paper reviews the literature made on certain properties and characteristics of a special type IASI-graph, the set-label of whose elements follow a definite pattern. Specifically, it summaries the results in following categories: Weak integer additive set-indexers of graphs, weak IASIs of graph operations, weak IASIs of certain graph products, induced weak IASIs of some associated graphs, Weak IASIs of some graphs and graph powers, and weakly uniform IASI graphs.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C90 Applications of graph theory
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References:

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