Abstract
We define a partial action of a group on a graph and their partial orbits and stabilizers for partial graphs. Further some relations between partial orbits and stabilizers are proved. A relation between α-transitivity and ÎČ-transitivity of a partial graph is proved where α is a partial action of a group G on the set of vertices and ÎČ is a partial action of a group G on the edge set of the graph.
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