%0 Journal Article
%T Graphs with <i>k</i>-Role Assignments
%A Yana Liu
%A Yongqiang Zhao
%J Open Journal of Discrete Mathematics
%P 177-184
%@ 2161-7643
%D 2017
%I Scientific Research Publishing
%R 10.4236/ojdm.2017.73016
%X For a given graph G, a k-role assignment of G is a surjective function ![\"\"](\"Edit_d1cca999-a2af-4efc-bf5d-b38d2f1ad213.bmp\")
such that ![\"\"](\"Edit_a4d37d51-d314-4211-95de-53a47c80e2fa.bmp\")
, 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.
%K Neighborhood
%K <
%K i>
%K k<
%K /i>
%K -Role Assignment
%K Restricted Size k-Role Assignment
%K <
%K i>
%K k<
%K /i>
%K -Threshold Close Role Assignment
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=77772