The Degree/diameter problem asks for the largest graphs given diameter and maximum degree. This problem has been extensively studied both for directed and undirected graphs, ando also for special classes of graphs. In this work we present the state of art of the degree/diameter problem for mixed graphs. c © 2015 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Org...

A directed strongly regular graph with parameters (n, k, t, λ, μ) is a k-regular directed graph with n vertices satisfying that the number of walks of length 2 from a vertex x to a vertex y is t if x = y, λ if there is an edge directed from x to y and μ otherwise. If λ = 0 and μ = 1 then we say that it is a mixed Moore graph. It is known that there are unique mixed Moore graphs with parameters ...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

Mixed states are of interest in quantum mechanics for modelling partial information. More recently categorical approaches to linguistics have also exploited the idea of mixed states to describe ambiguity and hyponym / hypernym relationships. In both these application areas the category Rel of sets and binary relations is often used as an alternative model. Selinger’s CPM construction provides t...

Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic polyhedral results. For mixed graphs, the notion of matching forest was proposed as a common generalization matchings branchings. In this paper, we propose edge cover covering counterpart forest, extend matching–covering framework graphs. While result...

In a connected graph G , the cardinality of smallest ordered set vertices that distinguishes every element V ( ) ? E is called mixed metric dimension . this paper we first establish exact value unicyclic which derived from structure We further consider graphs with edge disjoint cycles, where for each cycle C i define subgraph in only cycle. Applying result to then yields such The obtained formu...