| Title: | Edge-connectivity of strong products of graphs |
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| Authors: | ID Brešar, Boštjan (Author)
ID Špacapan, Simon (Author) |
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| Files: |  Discussiones_Mathematicae_Graph_Theory_2007_Bresar,_Spacapan_Edge-connectivity_of_strong_products_of_graphs.pdf (173,26 KB)
MD5: D34D8D01A73C898EFF74C0C05FF0E75C
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1365
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
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| Abstract: | The strong product ▫$G_1 \boxtimes G_2$▫ of graphs ▫$G_1$▫ and ▫$G_2$▫ is the graph with ▫$V(G_1) \times V(G_2)$▫ as the vertex set, and two distinct vertices ▫$(x_1,x_2)$▫ and ▫$(y_1,y_2)$▫ are adjacent whenever for each ▫$i\in \{1,2\}$▫ either ▫$x_i=y_i$▫ or ▫$x_iy_i \in E(G_i)$▫. In this note we show that for two connected graphs ▫$G_1$▫ and ▫$G_2$▫ the edge-connectivity ▫$\lambda(G_1 \boxtimes G_2)$▫ equals ▫$\min\{\delta(G_1\boxtimes G_2), \lambda(G_1)(|V(G_2)|+2|E(G_2)|), \lambda(G_2)(|V(G_1)|+2|E(G_1)|)\}$▫. In addition, we fully describe the structure of possible minimum edge cut sets in strong products of graphs. |
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| Keywords: | mathematics, graph theory, connectivity, strong product, graph product, separating set |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2007 |
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| Number of pages: | str. 333-343 |
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| Numbering: | Letn. 27, št. 2 |
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| PID: | 20.500.12556/DKUM-65338  |
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| ISSN: | 1234-3099 |
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| UDC: | 519.17 |
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| ISSN on article: | 1234-3099 |
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| COBISS.SI-ID: | 14368345 |
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| NUK URN: | URN:SI:UM:DK:IXOITPK7 |
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| Publication date in DKUM: | 31.03.2017 |
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| Views: | 1752 |
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| Downloads: | 414 |
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| Metadata: |    |
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| Categories: | Misc.
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