Publication Date

7-9-1973

Abstract

I. Sumner defined a graph to be point determining if and only if distinct points have distinct neighborhoods and he has characterized connected line-critical point determining graphs. Here a short alternate proof of his characterization is provided and arbitrary line-critical point determining graphs are then characterized. Next line-critical point distinguishing graphs are considered; a graph is point distinguishing if and only if it is the complement of a point determining graph. Finally line-critical graphs that are both point determining and point distinguishing are characterized.

II. Ore defined a graph to be geodetic if and only if there is a unique shortest path between any two points, and posed the problem of characterizing such graphs. Here this problem is studied in the context of oriented graphs and such geodetic orientations are characterized first for complete graphs (geodetic tournaments), then for complete bipartite and complete tripartite graphs, and finally for complete k-partite graphs.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Roger Charles Entringer

Second Committee Member

Edgar John Gilbert

Third Committee Member

Donald Ross Morrison

Language

English

Document Type

Dissertation

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