Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Discrete Mathematics and Combinatorics
Iterated Jump Graphs, Fran Herr, Legrand Jones Ii
Iterated Jump Graphs, Fran Herr, Legrand Jones Ii
Rose-Hulman Undergraduate Mathematics Journal
The jump graph J(G) of a simple graph G has vertices which represent edges in G where two vertices in J(G) are adjacent if and only if the corresponding edges in G do not share an endpoint. In this paper, we examine sequences of graphs generated by iterating the jump graph operation and characterize the behavior of this sequence for all initial graphs. We build on work by Chartrand et al. who showed that a handful of jump graph sequences terminate and two sequences converge. We extend these results by showing that there are no non-trivial repeating sequences of jump …
Iterated Line Graphs On Bi-Regular Graphs And Trees, Brenden Balch
Iterated Line Graphs On Bi-Regular Graphs And Trees, Brenden Balch
Rose-Hulman Undergraduate Mathematics Journal
In 1965, van Rooij and Wilf considered sequences of line graphs, in which they grouped sequences of line graphs into four categories. We’ll add to their research by presenting results on sequences of line graphs for star graphs and bi-regular graphs. We will then investigate slight variations of star graphs.