Results on the domination number and the total domination number of Lucas cubes - Saygi, Zülfükar (Ars mathematica contemporanea, 2020)
Lucas cubes are special subgraphs of Fibonacci cubes. For small dimensions, their domination numbers are obtained by direct search or integer linear programming. For larger dimensions some bounds on these numbers are given. In this work, we present the exact values of total domination number of small dimensional Lucas cubes and present optimization problems obtained from the degree information of Lucas cubes, whose solutions give better lower bounds on the domination numbers and total domination numbers of Lucas cubes.
Keywords: celoštevilsko linearno programiranje; dominacijsko število; domination number; Fibonacci cube; Fibonaccijeva kocka; integer linear programming; Lucas cube; Lucasova kocka; total domination number; totalno dominacijsko število