## Abstract

The study of graphs and networks often involves studying various parameters of the graph vertices, capturing different aspects of the graph structure, such as the vertex degrees or the distances between the vertices. Given an n-vertex graph G and a parameter of interest f, one may associate with G a vector F(G) = 〈f _{1} , …, f _{n} 〉 giving the value of f for each vertex. This vector can be thought of as the f-profile of the graph. This paper concerns the dual problem, where given an n-entry f-specification vector F = 〈f _{1} , …, f _{n} 〉, we need to decide whether it is possible to find a graph G realizing this specification, namely, whose f-profile F(G) conforms to F. The paper introduces the notion of graph realiziations and illustrates a number of example problems related to finding graph realiziations for given specifications.

Original language | English |
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Title of host publication | 25th International Colloquium, SIROCCO 2018, Revised Selected Papers |

Editors | Zvi Lotker, Boaz Patt-Shamir |

Publisher | Springer Verlag |

Pages | 3-13 |

Number of pages | 11 |

ISBN (Print) | 9783030013240 |

DOIs | |

State | Published - 2018 |

Event | 25th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2018 - Ma’ale HaHamisha, Israel Duration: 18 Jun 2018 → 21 Jun 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11085 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 25th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2018 |
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Country/Territory | Israel |

City | Ma’ale HaHamisha |

Period | 18/06/18 → 21/06/18 |

### Bibliographical note

Publisher Copyright:© Springer Nature Switzerland AG 2018.

### Funding

A. Bar-Noy—Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053 (the ARL Network Science CTA).

Funders | Funder number |
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ARL Network Science CTA | |

Army Research Laboratory | W911NF-09-2-0053 |