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Domination, independence and irredundance in graphs

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Topp J.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 1. Introduction........................................................................................................ 5 1.1. Purpose and scope................................................................................. 5 1.2. Basic graphtheoretical terms................................................................ 6 2. Domination, independence and irredundance in graphs................................ 9 2.1. Introduction and preliminaries.............................................................. 9 2.2. Domination parameters of vertex and edgedeleted subgraphs..... 15 2.3. Packing and covering numbers............................................................ 25 2.4. Conditions for equalities of domination parameters........................ 35 3. Well covered graphs........................................................................................ 46 3.1. Introduction and preliminary results..................................................... 46 3.2. The well coveredness of products of graphs..................................... 55 3.3. Well covered simplicial and chordal graphs...................................... 67 3.4. Well covered line and total graphs....................................................... 73 3.5. Well covered generalized Petersen graphs........................................ 78 3.6. Well irredundant graphs......................................................................... 80 4. Graphical sequences and sets of integers......................................................... 85 4.1. Dominationfeasible sequences........................................................... 86 4.2. Interpolation properties of domination parameters.......................... 91 References.................................................................................................................... 94

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1 Topp J.

1 1995

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Domination, independence and irredundance in graphs