id: 05711017
dt: j
an: 2010c.00399
au: Dana-Picard, Thierry
ti: Graph isomorphisms and matrix similarity: Switching between
representations.
so: Mont. Math. Enthus. 6, No. 3, 477-494 (2009).
py: 2009
pu: Information Age Publishing (IAP), Charlotte, NC; Department of Mathematical
Sciences, The University of Montana, Missoula, MT
la: EN
cc: K35 H65
ut: computer algebra systems; CAS; collegiate mathematics; graph theory; linear
algebra; matrices; representations; isomorphisms; inner mathematical
relations; graph theory; linear algebra; isomorphisms
ci:
li:
ab: Summary: A proof whether two graphs (possibly oriented graphs or
multigraphs, etc.) are isomorphic or not can be derived by various
methods. Some of them are reasonable for small numbers of vertices
and/or edges, but not for larger numbers. Switching from iconic
representation to a matrix representation transforms the problem of
Graph Theory into a problem in Linear Algebra. The support provided by
a Computer Algebra System is analyzed, in particular with regard to the
building of new mathematical knowledge through a transition from
graphical to algebraic representation. Moreover two important issues
are discussed: a. the need for more than one representation; b. the
direction of the switch between representations, which is non standard,
from graphical to algebraic.
rv: