Tjaša Paj (Author), Simon Špacapan (Author)

Abstract

Dokažemo, da je vsaka največja neodvisna množica v direktnem produktu sodega cikla ali lihe poti s poljubnim grafom $G$ unija množic $(A \times B$) in $(C \times D$), kjer sta $A$ in $C$ podmnožici cikla oziroma poti, ter $B$ in $D$ podmnožici grafa $G$. Prav tako diskutiramo strukturo največjih neodvisnih množic v direktnih produktih dreves s poljubnimi grafi.

Keywords

direktni produkt;neodvisna množica;direct product;independent set;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FS - Faculty of Mechanical Engineering
UDC: 519.17
COBISS: 17610841 Link will open in a new window
ISSN: 1234-3099
Views: 936
Downloads: 396
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: Slovenian
Secondary title: Največje neodvisne množice v direktnih produktih ciklov in dreves s poljubnimi grafi
Secondary abstract: The direct product of graphs ▫$G = (V(G),E(G))$▫ and ▫$H = (V(H),E(H))$▫ is the graph, denoted as ▫$G \times H$▫, with vertex set ▫$V(G \times H) = V(G )\times V(H)$▫, where vertices ▫$(x_1,y_1)$▫ and ▫$(x_2,y_2)$▫ are adjacent in ▫$G \times H$▫ if ▫$x_1x_2 \in E(G)$▫ and ▫$y_1y_2 \in E(H)$▫. Let ▫$n$▫ be odd and ▫$m$▫ even. We prove that every maximum independent set in ▫$P_n \times G$▫, respectively ▫$C_m \times G$▫, is of the form ▫$(A \times C) \cup (B \times D)$▫, where ▫$C$▫ and ▫$D$▫ are nonadjacent in ▫$G$▫, and ▫$A \cup B$▫ is the bipartition of ▫$P_n$▫ respectively ▫$C_m$▫. We also give a characterization of maximum independent subsets of ▫$P_n \times G$▫ for every even ▫$n$▫ and discuss the structure of maximum independent sets in ▫$T \times G$▫ where ▫$T$▫ is a tree.
Secondary keywords: direktni produkt;neodvisna množica;
URN: URN:SI:UM:
Type (COBISS): Scientific work
Pages: str. 675-688
Volume: ǂVol. ǂ35
Issue: ǂno. ǂ4
Chronology: 2015
ID: 9600332