A self-stabilizing algorithm for optimally efficient sets in graphs

Authors:
Sandra M. Hedetniemi;Stephen T. Hedetniemi;Hao Jiang;K. E. Kennedy;Alice A. Mcrae
Affiliations:
School of Computing, Clemson University, Clemson, SC 29634, United States;School of Computing, Clemson University, Clemson, SC 29634, United States;School of Computing, Clemson University, Clemson, SC 29634, United States;Department of Computer Science, Southern Wesleyan University, Central, SC 29630, United States;Department of Computer Science, Appalachian State University, Boone, NC 28608, United States
Venue:
Information Processing Letters
Year:
2012

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Abstract

The efficiency of a set S@?V in a graph G=(V,E), is defined as @e(S)=|{v@?V-S:|N(v)@?S|=1}|; in other words, the efficiency of a set S equals the number of vertices in V-S that are adjacent to exactly one vertex in S. A set S is called optimally efficient if for every vertex v@?V-S, @e(S@?{v})=