Now showing items 1-6 of 6

    • An algebraic approach to lifts of digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe; Sirán, Jozef (Elsevier, 2018)
      We present some applications of a new matrix approach for studying the properties of the lift of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, ...
    • An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Ryan, Joe (Elsevier, 2020)
      We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can ...
    • Degree diameter problem on honeycomb networks 

      Holub, Přemys; Miller, Mirka; Pérez Rosés, Hebert; Ryan, Joe (Elsevier, 2014-08-23)
      The degree diameter problem involves finding the largest graph (in terms of the number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction ...
    • From expanded digraphs to lifts of voltage digraphs and line digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe (Combinatorial Mathematics Society of Australasia (CMSA), 2017)
      In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship between lifted digraphs of voltage digraphs ...
    • On quotient digraphs and voltage digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe (Combinatorial Mathematics Society of Australasia (CMSA), 2017)
      We study the relationship between two key concepts in the theory of digraphs, those of quotient digraphs and voltage digraphs. These techniques contract or expand a given digraph in order to study its characteristics, or ...
    • Searching for large multi-loop networks 

      Feria Purón, Ramiro; Pérez Rosés, Hebert; Ryan, Joe (Elsevier, 2014)
      We describe and implement a computer-based method to find large multi-loop graphs with given degree and diameter. For some values of degree and diame- ter, our algorithm produces the largest known circulant graphs. We ...