## Abstract

A graph whose vertices have the same degree is called regular. Otherwise, the graph is irregular. In fact, various measures of irregularity have been proposed and examined. For a given graph G=(V,E) with V={v _{1} ,v _{2} ,…,v _{n} } and edge set E(G), d _{i} is the vertex degree where 1 ≤ i ≤ n. The irregularity of G is defined by irr(G)=∑ _{ v i v j ∈E(G) } |d _{i} −d _{j} |. A similar measure can be defined by irr _{2} (G)=∑ _{ v i v j ∈E(G) } (d _{i} −d _{j} ) ^{2} . The total irregularity of G is defined by irr _{t} (G)=[Formula presented]∑ _{ v i ,v j ∈V(G) } |d _{i} −d _{j} |. The variance of the vertex degrees is defined var(G)=[Formula presented]∑ _{i=1} ^{n} d _{i} ^{2} −([Formula presented]) ^{2} . In this paper, we present some Nordhaus–Gaddum type results for these measures and draw conclusions.

Original language | English |
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Pages (from-to) | 268-272 |

Number of pages | 5 |

Journal | Applied Mathematics and Computation |

Volume | 343 |

DOIs | |

Publication status | Published - 15 Feb 2019 |

## Keywords

- Degree
- Graph irregularity
- Nordhaus–Gaddum
- Regular graph
- Zagreb index