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    The basis number of the strong product of paths and cycles with bipartite graphs

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    1316032980.pdf (97.52Kb)
    Date
    2007
    Author
    Jaradat, M.M.M.
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    Abstract
    The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. MacLane [13] proved that a graph G is planar if and only if the basis number of G is less than or equal to 2. Ali [3] proved that the basis number of the strong product of a path and a star is less than or equal to 4. In this work, (1) We give an appropriate decomposition of trees. (2) We give an upper bound of the basis number of a cycle and a bipartite graph. (3) We give an upper bound of the basis number of a path and a bipartite graph. This is a generalization of Ali's result [3].
    DOI/handle
    http://dx.doi.org/10.35834/mjms/1316032980
    http://hdl.handle.net/10576/49112
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    • Materials Science & Technology [‎315‎ items ]

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