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The Basis Number of the Cartesian Product of a Path with a Circular Ladder, a Mobius Ladder and a Net

Mohammed M. M. Jaradat|Maref Y. Alzoubi
경북대학교 자연과학대학 수학과|2007.06|Kyungpook Mathematical Journal|제47권 제2호|pp. 165-174

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Abstract

The basis number of a graph G is the least positive integerk such that Ghas a k-fold basis. In this paper, we prove that the basis number of the cartesian productof a path with a circular ladder, a Mobius ladder and path with a net is exactly 3. This improves the upper bound of the basis number of these graphs for a general theorem on the cartesian product of graphs obtained by Ali and Marougi, see [2]. Also, by this general result, the cartesian product of a theta graph with a Mobius ladder is at most 5. But insection 3 we prove that it is at most 4.

참고문헌 (12)

  1. "The basis number of the direct product of paths and cycles", pp.155~163 (1989)
  2. "The basis number of the cartesian product of somegraphs", pp.123~134 (1992)
  3. "The basis number of the cartesian product of somespecial graphs", pp.83~100 (1993)
  4. "The basis number of the powers of the completegraph", 188(1-3), pp.13~25 (1998)
  5. "The basis number of the composition of thetagraph with stars and wheels", 103(3), pp.201~209 (2004)
  6. "The basis number of n-cube", pp.95~33 100 (1982)
  7. "Graph theory with applications" (1976), America ElsevierPublishing Co Inc
  8. "Graph theory", 173 (1997), Springer-Verlage,New York
  9. "The basis number of the composition of graphs", pp.43~60 (1994), Istanbul Univ
  10. "Product graphs: Structure and recognition, Wiley-Interscience Series in Discrete Mathematics and Optimization" (2000)
  11. "On the basis number of the direct product of graphs", 27, pp.293~306 (2003)
  12. "The basis number of the direct product of a theta graph and a path", 75, pp.105~111 (2005)

관련 논문AI추천

The Basis Number of the Lexicographic Product of DifferentLadders with Paths and CyclesMaref Y. M. Alzoubi, Reem A. Al-Ta’ani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제2호On the Basis Number of the Semi-Strong Product of Bipartite Graphs with CyclesMaref Y. Alzoubi, M. M. M. Jaradat경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제1호An upper bound of the basis number of the semi-strong product of cycles with bipartite graphsMohammed M. M. Jaradat대한수학회 · 대한수학회보2007 · 제44권 제3호Independent metric dimension of Möbius laddersB. Suganya, S. Arumugam장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제2호The bondage number of $C_3 \times C_n$손무영, 정현석, Yuan Xudong대한수학회 · 대한수학회지2007 · 제44권 제6호Hub number of some wheel related graphsAnand P. Barangi, B. Basavanagoud, Ismail Naci CANGUL장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호

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