Name
Abstract | ||
|---|---|---|
If G is a connected graph, then HA(G)=∑u≠v(deg(u)+deg(v))/d(u,v) is the additively Harary index and HM(G)=∑u≠vdeg(u)deg(v)/d(u,v) the multiplicatively Harary index of G. G is an apex tree if it contains a vertex x such that G−x is a tree and is a k-apex tree if k is the smallest integer for which there exists a k-set X⊆V(G) such that G−X is a tree. Upper and lower bounds on HA and HM are determined for apex trees and k-apex trees. The corresponding extremal graphs are also characterized in all the cases except for the minimum k-apex trees, k≥3. In particular, if k≥2 and n≥6, then HA(G)≤(k+1)(3n2−5n−k2−k+2)/2 holds for any k-apex tree G, equality holding if and only if G is the join of Kk and K1,n−k−1. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.dam.2015.01.044 | Discrete Applied Mathematics |
Keywords | Field | DocType |
Additively Harary index,Multiplicatively Harary index,Apex tree,k-apex tree,Harmonic number | Integer,Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Upper and lower bounds,Apex (geometry),Harmonic number,Connectivity,Mathematics | Journal |
Volume | ISSN | Citations |
189 | 0166-218X | 4 |
PageRank | References | Authors |
0.46 | 14 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kexiang Xu | 1 | 72 | 11.43 |
| Jinlan Wang | 2 | 4 | 0.46 |
| Kinkar Ch. Das | 3 | 208 | 30.32 |
| sandi klavžar | 4 | 542 | 58.66 |