# Graphs and Applications_ An Introductory Approach

@inproceedings{Aldous2001GraphsAA, title={Graphs and Applications\_ An Introductory Approach}, author={Joan Aldous and Robin J. Wilson}, year={2001} }

1 Introduction.- 1.1 Graphs, Digraphs and Networks.- 1.2 Classifying Problems.- 1.3 Seeking Solutions.- 2 Graphs.- 2.1 Graphs and Subgraphs.- 2.2 Vertex Degrees.- 2.3 Paths and Cycles.- 2.4 Regular and Bipartite Graphs.- 2.5 Case Studies.- Four Cubes Problem.- Social Networks.- Exercises 2.- 3 Eulerian and Hamiltonian Graphs.- 3.1 Exploring and Travelling.- 3.2 Eulerian Graphs.- 3.3 Hamiltonian Graphs.- 3.4 Case Studies.- Dominoes.- Diagram-Tracing Puzzles.- Knight's Tour Problem.- Gray Codes…

## 107 Citations

Generische Bücher - ein graphentheoretisches Modell zur logischen Strukturierung von Büchern in on-Demand-Publikationsprozessen

- Philosophy
- 2002

XIII A. Objective and scientific context XIII B. Methodology and innovation XIV C. Results and potential extension XVI 1 EINLEITUNG 1 1.1 Untersuchungsgegenstand und Ziel der Arbeit 1 1.2 Gliederung…

On the survivable network design problem with mixed connectivity requirements

- MathematicsAnnals of Operations Research
- 2019

This paper proposes to design a (k, l)-connected network with minimum cost, by presenting two integer programming formulations and a cutting plane algorithm and modifying the conclusion by changing from k to k, and formally proving it.

Centrality measures for node-weighted networks via line graphs and the matrix exponential

- Computer ScienceNumer. Algorithms
- 2021

It is shown that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled.

Spanning tree based method for a social network analysis

- Computer Science2015 IEEE/ACS 12th International Conference of Computer Systems and Applications (AICCSA)
- 2015

A promising approach based on the contraction of nodes that facilitate the enumeration of spanning trees in a social network containing a large number of individuals and interactions is proposed.

Elegant labeling of sun graphs and helm graphs

- Mathematics
- 2021

This paper shows that sun graph n-sun and helm graph Hn, where n is an odd integer at least 3, are elegant.

Weakly Connected Domination in Graphs Resulting from Some Graph Operations

- Mathematics
- 2011

Let G = (V (G),E(G)) be a connected undirected graph. The closed neighborhood of any vertex v ∈ V (G) is NG[v] = {u ∈ V (G) : uv ∈ E(G)} ∪ {v}. For C ⊆ V (G), the closed neighborhood of C is N [C] =…

On Edge Addition Problem with some graphs

- Mathematics
- 2018

The two questions that: how many edges at least have to be added to the network to ensure the message within the effective bounds, and how large message delay will be increased when faults occur, can…

Fault diameters of graph products and bundles

- Mathematics
- 2010

Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many…

Mixed fault diameter of Cartesian graph bundles II

- MathematicsArs Math. Contemp.
- 2015

It is proved that if q > 0, then D ( p + 1, q ) ( G )’s diameter is the maximum diameter among all subgraphs obtained from graph G by deleting p vertices and any- q edges.

Content Placement in Cache Networks Using Graph Coloring

- Computer ScienceIEEE Systems Journal
- 2020

By employing the proposed scheme in a typical network, the load on the backhaul links is reduced significantly in average compared to the conventional scheme and some previously proposed schemes.