Sequence mixed graphs

TL;DR

This paper introduces sequence mixed graphs, a generalization of sequence graphs and iterated line digraphs, which are useful for constructing dense graphs with favorable degree/diameter ratios and analyzing their distance parameters.

Contribution

It defines sequence mixed graphs, establishes their usefulness in degree/diameter problems, and presents a method to construct them via vertex identification in iterated line digraphs.

Findings

Sequence mixed graphs generalize existing graph structures.

They can be used to construct dense graphs with good degree/diameter ratios.

Results include bounds and properties of diameter and average distance.

Abstract

A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures are proven to be useful in the problem of constructing dense graphs or digraphs, and this is related to the degree/diameter problem. Thus, our generalized approach gives rise to graphs that have also good ratio order/diameter. Moreover, we propose a general method for obtaining a sequence mixed digraph by identifying some vertices of a certain iterated line digraph. As a consequence, some results about distance-related parameters (mainly, the diameter and the average distance) of sequence mixed graphs are presented.