Graphs with k-Role Assignments ()
ABSTRACT
For a given graph
G, a
k-role assignment of
G is a surjective function
such that
, where
N(x) and
N(y) are the neighborhoods of
x and
y, respectively. Furthermore, as we limit the number of different roles in the neighborhood of an individual, we call
r a restricted size
k-role assignment. When the hausdorff distance between the sets of roles assigned to their neighbors is at most 1, we call
r a
k-threshold close role assignment. In this paper we study the graphs that have
k-role assignments, restricted size
k-role assignments and
k-threshold close role assignments, respectively. By the end we discuss the maximal and minimal graphs which have
k-role assignments.
Share and Cite:
Liu, Y. and Zhao, Y. (2017) Graphs with
k-Role Assignments.
Open Journal of Discrete Mathematics,
7, 177-184. doi:
10.4236/ojdm.2017.73016.
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