# This report was written for the April 15,2025 version of ExpSP.txt



#####################################################################
# Vertex Transitive Graphs
#####################################################################

## Tests were run by defining these variables:
L:=VtxTransNumLeaves(G):
tau:=NumSpanTree(G):

######## Torus ########

## r = 5 ##
G:=Torus(100,5):
evalf(L/tau);
# Output: ~ 140       TRUE VALUE
evalf(EstAvgNumLeaves(Torus,100,5,100));   # K=100
# Output: ~ 139.39    ESTIMATE

## r = 4 ##
G:=Torus(100,4):
evalf(L/tau);
# Output: ~ 113.04     TRUE VALUE
evalf(EstAvgNumLeaves(Torus,100,4,300));   # K=300
# Output: ~ 112.81     ESTIMATE

## r = 3 ##
G:=Torus(100,3):
evalf(L/tau);
# Output: ~ 113.04     TRUE VALUE
evalf(EstAvgNumLeaves(Torus,100,3,500));   # K=500 
# Output: ~ 112.81     ESTIMATE


######## Gnr ########

## r = 6 ##
G:=Gnr(100,5):
evalf(L/tau);
# Output: ~ 35.5             TRUE VALUE
evalf(EstAvgNumLeaves(Gnr,100,6,500));   # K=500
# Output: ~ 35.57            ESTIMATE


## r = 5 ##
G:=Gnr(100,5):
evalf(L/tau);
# Output: ~ 34.94         TRUE VALUE
evalf(EstAvgNumLeaves(Gnr,100,5,500));   # K=500
# Output: ~ 35            ESTIMATE

## r = 4 ##
G:=Gnr(100,4):
evalf(L/tau);
# Output: ~ 34          TRUE VALUE
evalf(EstAvgNumLeaves(Gnr,100,4,500));   # K=500
# Output: ~ 33.91       ESTIMATE

## r = 3 ##
G:=Gnr(100,3):
evalf(L/tau);
# Output: ~ 32.15       TRUE VALUE
evalf(EstAvgNumLeaves(Gnr,100,3,500));   # K=500
# Output: ~ 32.21       ESTIMATE


## r = 2 ##
G:=Gnr(100,2):
evalf(L/tau);
# Output: ~ 27.35       TRUE VALUE
evalf(EstAvgNumLeaves(Gnr,100,2,1000));   # K=1000
# Output: ~ 27.38    ESTIMATE

#####################################################################
# Non-Vertex Transitive Graphs
#####################################################################

##### Test were run by defining these variables: 
L:=NumLeaves(G):
tau:=NumSpanTree(G):

######## Hnr ########

## r = 6 ##
G:=Hnr(100,6):
evalf(L/tau);
# Output: ~ 35.58   TRUE VALUE
evalf(EstAvgNumLeaves(Hnr,100,6,));   # K=300
# Output: ~ 35.57    ESTIMATE

## r = 5 ##
G:=Hnr(100,5):
evalf(L/tau);
# Output: ~ 35.01   TRUE VALUE
evalf(EstAvgNumLeaves(Hnr,100,5,300));   # K=300
# Output: ~ 35.08    ESTIMATE

## r = 4 ##
G:=Hnr(100,4):
evalf(L/tau);
# Output: ~ 34.05   TRUE VALUE
evalf(EstAvgNumLeaves(Hnr,100,4,300));   # K=300
# Output: ~ 34.05    ESTIMATE

## r = 3 ##
G:=Hnr(100,3):
evalf(L/tau);
# Output: ~ 32.19    TRUE VALUE
evalf(EstAvgNumLeaves(Hnr,100,3,300));    # K=300
# Output: ~ 32.36    ESTIMATE

## r = 2 ##
G:=Hnr(100,2):
evalf(L/tau);
# Output: ~ 27.37       TRUE VALUE
evalf(EstAvgNumLeaves(Hnr,100,2,500));   # K=500
# Output: ~ 27.5     ESTIMATE

######## GridGr ########

## r = 5 ##
G:=GridGr(100,5):
evalf(L/tau);
# Output: ~ 133.55   TRUE VALUE
evalf(EstAvgNumLeaves(GridGr,100,5,));   # K=200
# Output: ~ 133.32    ESTIMATE

## r = 4 ##
G:=GridGr(100,4):
evalf(L/tau);
# Output: ~ 106.41   TRUE VALUE
evalf(EstAvgNumLeaves(GridGr,100,4,200));   # K=200
# Output: ~ 106.43    ESTIMATE

## r = 3 ##
G:=GridGr(100,3):
evalf(L/tau);
# Output: ~ 78.21   TRUE VALUE
evalf(EstAvgNumLeaves(GridGr,100,3,300));   # K=300
# Output: ~ 78.73    ESTIMATE