Abstract
Let Sz(G) and ξc(G) be the Szeged index and the eccentric connectivity index of a graph G, respectively. In this paper we obtain a lower bound on Sz(T)−ξc(T) by double counting on some matrix and characterize the extremal graphs. From this result we compare the Szeged index and the eccentricity connectivity index of trees. For bipartite graphs we also compare the Szeged index and the eccentricity connectivity index. Moreover, we show that Sz(G)−ξc(G)≥−4 for bipartite graphs and this result is not true in the general case. Finally, we classify the bipartite graphs G in which Sz(G)−ξc(G)∈{−4,−3,−2,−1,0,1,2}.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
