Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900749 | Applied Mathematics and Computation | 2018 | 8 Pages |
Abstract
For a connected graph G, with degG(vi) and ÉG(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)=â|ÉG(vj)âÉG(vi)| and irrt(G)=â|degG(vj)âdegG(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)â¯>â¯N(G) holds for almost all graphs. Some graphs are constructed for which N(G)=irrt(G). Moreover, we prove that N(T)â¯>â¯irrt(T) for any tree T of order nâ¯â¥â¯15 with diameter dâ¯â¥â¯2n/3 and maximum degree 3.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Kexiang Xu, Xiaoqian Gu, Ivan Gutman,