Map coloring with MRV and Degree heuristics in Python
Although not familiar with MRV and degree heuristics, i can make some remarks about the Python code style:

Loops can be made more Pythonic

for i in range(len(self.adjacencyList[initialNode])):
    childNode = self.adjacencyList[initialNode][i]


should be written as: 

for childNode in self.adjacencyList[initialNode]:


Conditionals

if(self.isSafe(childNode, c) == True):


should be

if self.isSafe(childNode, c):


method isSafe

def isSafe(self, node, c):
    for i in range(len(self.adjacencyList[node])):
        if(self.color[self.adjacencyList[node][i]] == c):
            return False
    return True


could be:

def isSafe(self, node, c):
    for adjacency in self.adjacencyList[node]:
        if self.color[adjacency] == c:
            return False
    return True


or even, more Pythonic, but a bit cryptic:

def isSafe(self, node, c):
    # return True if all node neighbours colors differ from c
    return all([self.color[adj] != c for adj in self.adjacencyList[node]])        


Data structure

The repetition of the keys in the adjacencyList and color
suggest a data structure like the following, although this requires a 
lot changes in the existing code:

nodes = {
    'WA' : {'color' : 0, 'neighbours' : ['NT', 'SA']},
    'NT' : {'color' : 0, 'neighbours' : ['WA', 'SA', 'Q']},
    'SA' : {'color' : 0, 'neighbours' : ['WA', 'NT', 'Q', 'NSW', 'V']},
    'Q'  : {'color' : 0, 'neighbours' : ['NT', 'SA', 'NSW']},
    'NSW': {'color' : 0, 'neighbours' : ['SA', 'Q', 'V']},
    'V'  : {'color' : 0, 'neighbours' : ['SA', 'T', 'NSW']},
    'T'  : {'color' : 0, 'neighbours' : ['V']},
}    


Others:


self.nodeSequence is not used
self.totalNodes is not used
minCount = 0 was edited out in getNodeWithMRV but should be there, or if (countColor &lt; minCount) should be if (countColor &lt; 0)
pickNode is called only once with a constant argument '', and can therefor be made simpler 
getNodeWithMRV will always return '' because countColor will never be smaller than 0.
the ; at the end of adjacencyList = ... and color = ... an origin in another language :-)