Geodesic
On Maximally Irregular Graphs
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 3

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Let $G$ be a connected graph with maximum degree $\Delta(G)$. The {\it irregularity index} $t(G)$ of $G$ is defined as the number of distinct terms in the degree sequence of $G$. We say that $G$ is {\it maximally irregular} if $t(G)=\Delta(G)$. The purpose of this note, apart from pointing out that every highly irregular graph is maximally irregular, is to establish upper bounds on the size of maximally irregular graphs and maximally irregular triangle-free graphs.
Classification : 97K30 
Simon Mukwembi. On Maximally Irregular Graphs. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2013_36_3_a14/
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     author = {Simon Mukwembi},
     title = {On {Maximally} {Irregular} {Graphs}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2013},
     volume = {36},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_3_a14/}
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