Degree Name

MS (Master of Science)


Mathematical Sciences

Date of Award


Committee Chair or Co-Chairs

James Boland

Committee Members

Don Hong, Janice Huang


The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some results based on these definitions.

Document Type

Thesis - Open Access


Copyright by the authors.

Included in

Mathematics Commons