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Published December 5, 1997 | public
Journal Article

Constructing status injective graphs

Abstract

The status, or distance sum, of a given vertex v in a graph is defined by s(v) = ∑_(u ≠ v)d(u, v) where d(u, v) is the distance from a vertex u to v. We show that every graph is the induced subgraph of a graph whose vertices all have distinct stati. Using this result we then construct a family of graphs which have consecutive integers for their stati. This settles the question raised by Harary and Buckley about whether there exist graphs whose stati are consecutive integers. We also use the above constructions to find families of non-isomorphic graphs with the same stati.

Additional Information

© 1997 Elsevier. Received 15 July 1996; revised 21 October 1996.

Additional details

Created:
August 19, 2023
Modified:
October 25, 2023