In this paper, for the purpose of measuring the non-self-centrality extent of non-self- centered graphs, a novel eccerttricity-based invariant, named as non-self-centrality number （NSC num- ber for short）, of a grap...In this paper, for the purpose of measuring the non-self-centrality extent of non-self- centered graphs, a novel eccerttricity-based invariant, named as non-self-centrality number （NSC num- ber for short）, of a graph G is defined as follows： N（G） =∑vi,vj∈V（G）｜ei-ej｜ where the summation goes over all the unordered pairs of vertices in G and ei is the eccentricity of vertex vi in G, whereas the invariant will be called third Zagreb eccentricity index if the summation only goes over the adja- cent vertex pairs of graph G. In this paper, we determine the lower and upper bounds on N（G） and characterize the corresponding graphs at which the lower and upper bounds are attained. Finally we propose some attractive research topics for this new invariant of graphs.展开更多
基金Supported by NSFC(Grant No.11201227)China Postdoctoral Science Foundation(Grant Nos.2013M530253,2014T70512)+2 种基金Natural Science Foundation of Jiangsu Province(Grant No.BK20131357)National Research Foundation funded by the Korean government(Grant Nos.2013R1A1A2009341)TUBITAK and Scientific Research Project Office(BAP)of Sel?uk University
文摘In this paper, for the purpose of measuring the non-self-centrality extent of non-self- centered graphs, a novel eccerttricity-based invariant, named as non-self-centrality number （NSC num- ber for short）, of a graph G is defined as follows： N（G） =∑vi,vj∈V（G）｜ei-ej｜ where the summation goes over all the unordered pairs of vertices in G and ei is the eccentricity of vertex vi in G, whereas the invariant will be called third Zagreb eccentricity index if the summation only goes over the adja- cent vertex pairs of graph G. In this paper, we determine the lower and upper bounds on N（G） and characterize the corresponding graphs at which the lower and upper bounds are attained. Finally we propose some attractive research topics for this new invariant of graphs.
