Contributions to the Study of Contemporary Domination Invariants of GraphsBrešar, Boštjan (Mentor) Dravec, Tanja (Komentor) Grundy dominationGrundy total dominationZ-Grundy dominationL-Grundy dominationconvex dominationisometric dominationtotal dominationtreessplit graphsinterval graphsSierpi\'nski graphsKneser graphsmodular decompositiondominating pair graphsCartesian productThis doctoral dissertation is devoted to contemporary domination concepts, such as the Grundy domination, the convex domination, the isometric domination and the total domination. Our main focus is to study their structure and algorithmic properties. Four Grundy domination invariants are presented, namely the Grundy domination number, the Grundy total domination number, the Z-Grundy domination number, and the L-Grundy domination number. Some bounds and properties of Grundy domination invariants are proven. All four Grundy domination parameters are studied on trees, bipartite distance-hereditary graphs, split graphs, interval graphs, Sierpi\'nski graphs, Kneser graphs and $P_4$-tidy graphs. Graphs with equal total domination number and Grundy total domination number are investigated. Convex domination and isometric domination are studied on (weak) dominating pair graphs. For the chordal dominating pair graphs we present a polynomial algorithm to compute the convex domination number, and prove the NP-completeness of the corresponding decision problem for the chordal weak dominating pair graphs. For the isometric domination number of weak dominating pair graphs an efficient algorithm is presented. Total domination is studied on the Cartesian product of graphs. We dedicate ourselves to graphs for which the equality holds in Ho's theorem, which states that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers.T. Kos]20192019-04-02 17:20:58Doktorsko delo/naloga73378UDK: 519.17(043.3)COBISS_ID: 302222080NUK URN: URN:SI:UM:DK:W7R53FG8sl