Multiple input multiple output (MIMO) wireless
mesh networks (WMNs) aim to provide the last-mile broadband
wireless access to the Internet. Along with the algorithmic development
for WMNs, some fundamental mathematical problems
also emerge in various aspects such as routing, scheduling, and
channel assignment, all of which require an effective mathematical
model and rigorous analysis of network properties. In
this paper, we propose to employ Cartesian product of graphs
(CPG) as a multichannel modeling approach and explore a
set of unique properties of triangular WMNs. In each layer of
CPG with a single channel, we design a node coordinate scheme
that retains the symmetric property of triangular meshes and
develop a function for the assignment of node identity numbers
based on their coordinates. We also derive a necessary-sufficient
condition for interference-free links and combinatorial formulas
to determine the number of the shortest paths for channel
realization in triangular WMNs
