Acta Orientalia Vilnensia
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    On the Betti numbers and gracefulness of some planar graphs

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    In this article bipartite planar graphs St_r are investigated, r the number of their plane regions. Bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to such graphs are discussed. We prove that r is related to algebraic invariants of the graph arising from the projective resolution of the edge ideal. We also deal with labeling methods for some graphs and show that graphs St_r admit a graceful numbering of their edges

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    Acta Orientalia Vilnensia
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