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Constructing status injective graphs

Pachter, Lior (1997) Constructing status injective graphs. Discrete Applied Mathematics, 80 (1). pp. 107-113. ISSN 0166-218X. https://resolver.caltech.edu/CaltechAUTHORS:20170309-143338663

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0166-218X(97)00073-5DOIArticle
http://www.sciencedirect.com/science/article/pii/S0166218X97000735PublisherArticle
ORCID:
AuthorORCID
Pachter, Lior0000-0002-9164-6231
Additional Information:© 1997 Elsevier. Received 15 July 1996; revised 21 October 1996.
Issue or Number:1
Record Number:CaltechAUTHORS:20170309-143338663
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170309-143338663
Official Citation:Lior Pachter, Constructing status injective graphs, Discrete Applied Mathematics, Volume 80, Issue 1, 1997, Pages 107-113, ISSN 0166-218X, http://dx.doi.org/10.1016/S0166-218X(97)00073-5. (http://www.sciencedirect.com/science/article/pii/S0166218X97000735)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74998
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:10 Mar 2017 03:30
Last Modified:24 Feb 2020 10:30

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