Name
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={v1,v2,…,vn} and edge set E(G), di is the vertex degree where 1 ≤ i ≤ n. The irregularity of G is defined by irr(G)=∑vivj∈E(G)|di−dj|. A similar measure can be defined by irr2(G)=∑vivj∈E(G)(di−dj)2. The total irregularity of G is defined by irrt(G)=12∑vi,vj∈V(G)|di−dj|. The variance of the vertex degrees is defined var(G)=1n∑i=1ndi2−(2mn)2. In this paper, we present some Nordhaus–Gaddum type results for these measures and draw conclusions. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.amc.2018.09.057 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Regular graph,Graph irregularity,Nordhaus–Gaddum,Degree,Zagreb index | Graph,Combinatorics,Vertex (geometry),Mathematical analysis,Regular graph,Degree (graph theory),Mathematics | Journal |
Volume | ISSN | Citations |
343 | 0096-3003 | 0 |
PageRank | References | Authors |
0.34 | 13 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuede Ma | 1 | 8 | 0.96 |
| Shu-juan Cao | 2 | 77 | 5.86 |
| Yongtang Shi | 3 | 511 | 55.83 |
| Matthias Dehmer | 4 | 863 | 104.05 |
| Chengyi Xia | 5 | 149 | 20.94 |