Name
Abstract | ||
|---|---|---|
For a connected graph G, with degG(vi) and ɛG(vi) denoting the degree and eccentricity of the vertex vi, the non-self-centrality number and the total irregularity of G are defined as N(G)=∑|ɛG(vj)−ɛG(vi)| and irrt(G)=∑|degG(vj)−degG(vi)|, with summations embracing all pairs of vertices. In this paper, we focus on relations between these two structural invariants. It is proved that irrt(G) > N(G) holds for almost all graphs. Some graphs are constructed for which N(G)=irrt(G). Moreover, we prove that N(T) > irrt(T) for any tree T of order n ≥ 15 with diameter d ≥ 2n/3 and maximum degree 3. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.amc.2018.05.058 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Degree (of vertex),Eccentricity (of vertex),Total irregularity,Non-self-centrality number | Graph,Combinatorics,Vertex (geometry),Mathematical analysis,Centrality,Invariant (mathematics),Degree (graph theory),Connectivity,Mathematics | Journal |
Volume | ISSN | Citations |
337 | 0096-3003 | 0 |
PageRank | References | Authors |
0.34 | 4 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kexiang Xu | 1 | 72 | 11.43 |
| Xiaoqian Gu | 2 | 0 | 0.34 |
| I. Gutman | 3 | 9 | 2.80 |