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An investigation of the extent to which line symmetry and regularity imply point symmetry. First are given some conditions on the number of vertices and the degree of regularity under which line symmetry and regularity imply point symmetry; then general methods for constructing graphs that are line symmetric, and finally, a summary of what is known about the number of vertices that a regular line symmetric graph that is not point symmetric can have. The Memorandum concludes with a list of unsolved problems in this area

This report is part of the RAND Corporation research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.