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Note on irregular graphs

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2018
Gutman.pdf (236.1Kb)
Authors
Gutman, Ivan
Réti, Tamás
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Abstract
Let G be a graph with vertex set V(G) and edge set E(G). For v ∈ V(G), by dG(v) is denoted the degree of the vertex v. A graph in which not all vertices have equal degrees is said to be irregular. Different quantitative measures of irregularity have been proposed, of which the Albertson index irr(G) = Σuv∈E(G) |dG(u) − dG(v)| is the most popular. We compare irr(G) with the recently introduced sigma-index σ(G) = Σuv∈E(G)[dG(u) − dG(v)]2 and show that in the general case these are incomparable. Graphs in which |dG(u)−dG(v)| = 1 holds for all uv ∈ E(G) are called stepwise irregular (SI). Severalmethods for constructing SI graphs are described.
Keywords:
degree (of vertex) / irregularity (of graph) / stepwise irregular graph / Albertson index / σ index
Source:
Bulletin T.CLI de l’Académie serbe des sciences et des arts, 2018, 5-16
Publisher:
  • Beograd : Académie Serbe des sciences et des arts
Note:
  • Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles. Sciences mathématiques. 43, 151 (2018).

ISSN: 0561-7332

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_dais_9080
URI
https://dais.sanu.ac.rs/123456789/9080
Collections
  • Classe des sciences mathematiques et naturelles
Institution/Community
Cрпска академија наука и уметности / Serbian Academy of Sciences and Arts
Gutman, I.,& Réti, T.. (2018). Note on irregular graphs. in Bulletin T.CLI de l’Académie serbe des sciences et des arts
Beograd : Académie Serbe des sciences et des arts., 5-16.
https://hdl.handle.net/21.15107/rcub_dais_9080
Gutman I, Réti T. Note on irregular graphs. in Bulletin T.CLI de l’Académie serbe des sciences et des arts. 2018;:5-16.
https://hdl.handle.net/21.15107/rcub_dais_9080 .
Gutman, Ivan, Réti, Tamás, "Note on irregular graphs" in Bulletin T.CLI de l’Académie serbe des sciences et des arts (2018):5-16,
https://hdl.handle.net/21.15107/rcub_dais_9080 .

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