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Uniquely Bipancyclic Graphs

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Pancyclic and Bipancyclic Graphs

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Abstract

In this chapter we look at the problem of uniquely bipancyclic graphs, that is bipartite graphs that contain exactly one cycle of each length from 4 up to the number of vertices. If such a graph contains c cycles, their lengths are 4, 6, …, 2c + 2, so the graph has 2c + 2 vertices; moreover the sum of the lengths of the cycles (total number of edges in the cycles, with multiple appearances in different cycles counted multiply) is \(4 + 6 + \cdots + (2c + 2) = c^{2} + 3c\). We shall denote this by s(c).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Gordon State College, Barnesville, GA, USA

    John C. George

  2. Department of Mathematics, University of West Georgia, Carrollton, GA, USA

    Abdollah Khodkar

  3. Department of Mathematics, Southern Illinois University, Evansville, IN, USA

    W. D. Wallis

Authors
  1. John C. George
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  2. Abdollah Khodkar
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  3. W. D. Wallis
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George, J.C., Khodkar, A., Wallis, W.D. (2016). Uniquely Bipancyclic Graphs. In: Pancyclic and Bipancyclic Graphs. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-31951-3_7

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