Geodesic
On graph irregularity indices with particular regard to degree deviation
Filomat, Tome 35 (2021) no. 11, p. 3689

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DOI

Let G = (V,E), V = {v1, v2, . . . , vn}, be a simple connected graph of order n and size m, with vertex degree sequence d1 ≥ d2 ≥ · · · ≥ dn. A graph G is said to be regular if d1 = d2 = · · · = dn. Otherwise it is irregular. In many applications and problems it is important to know how irregular a given graph is. A quantity called degree deviation S(G) = ∑n i=1 ∣∣∣di − 2mn ∣∣∣ can be used as an irregularity measure. Some new lower bounds for S(G) are obtained. A simple formula for computing S(G) for connected bidegreed graphs is derived also. Besides, two novel irregularity measures are introduced
DOI : 10.2298/FIL2111689R
Classification : 05C12, 05C50
Keywords: Irregularity of graph, degree deviation, vertex degree 
T Réti; I Milovanović; E Milovanović; M Matejić. On graph irregularity indices with particular regard to degree deviation. Filomat, Tome 35 (2021) no. 11, p. 3689 . doi: 10.2298/FIL2111689R
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     title = {On graph irregularity indices with particular regard to degree deviation},
     journal = {Filomat},
     pages = {3689 },
     year = {2021},
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     doi = {10.2298/FIL2111689R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2111689R/}
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