Abstract
LetG be a simple connected graph. Theeccentricity e(u) of a vertexu inG is given bye(u)=max {d(u,v): v?V(G)}. A vertexv is called aperipheral vertex ofG ife(v)=dia(G). A vertexv is called aneccentric vertex ofG ifd(v,c)=e(C) for some center vertexc ofG. LetP(G) andEC(G) denote the sets of peripheral vertices and eccentric vertices ofG, respectively. The main result in this paper is a discription of general classes of graphs for whichP(G)=EC(G). In particular, we give necessary and sufficient conditions for a graphG withdia(G)=2r(G) ordia(G)=2r(G)?1 to satisfyP(G)=EC(G). Also, we present several graphs which then are used to show that all possible set-inclusion relations betweenP(G) andEC(G) may occur.
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.
