Date of Award
2011
Publisher
North Dakota State University
Document Type
Thesis
Degree Awarded
Master of Science (MS)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
Shreve, Warren E.
Description
It can be shown that any symmetric (0, 1)-matrix A with tr A = 0 can be interpreted as the adjacency matrix of a simple, finite graph. The square of an adjacency matrix A2 = (si1) has the property that Sij represents the number of walks of length two from vertex i to vertex j. With this information, the motivating question behind this paper was to determine what conditions on a matrix S are needed to have S = A(G)2 for some graph G. Structural results imposed by the matrix S include detecting bipartiteness or connectedness, counting four cycles and determining plausible neighborhoods of vertices. Some characterizations will be given and the problem of when S represents several non-isomorphic graphs is also explored.
Recommended Citation
Kranda, Daniel Joseph, "The Square of Adjacency Matrices" (2011). Mathematics. 21.
https://digitalcommons.ndsu.edu/mathematics/21
Rights
NDSU policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/33250