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Abstract
(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)
An ......-labeling of a graph ...... is a function ...... from the vertex set ...... to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The ......-labeling number denoted by ...... of ...... is the minimum range of labels over all such labeling. In this article, it is shown that, for an interval graph ......, the upper bound of ...... is ......, where ...... and ...... represents the maximum degree of the vertices and size of maximum clique respectively. An ...... time algorithm is also designed to ......-label a connected interval graph, where ...... and ...... represent the number of edges and vertices respectively. Extending this idea it is shown that ...... for circular-arc graph.