3 research outputs found
A characterization of graphs with at most four boundary vertices
Steinerberger defined a notion of boundary for a graph and established a
corresponding isoperimetric inquality. Hence, "large" graphs have more boundary
vertices. In this paper, we first characterize graphs with three boundary
vertices in terms of two infinite families of graphs. We then completely
characterize graphs with four boundary vertices in terms of eight families of
graphs, five of which are infinite. This parallels earlier work by Hasegawa and
Saito as well as M\"uller, P\'or, and Sereni on another notion of boundary
defined by Chartrand, Erwin, Johns, and Zhang.Comment: 16 pages, 9 figure