**Affiliation:**

School of Electrical Engineering and Computer Science

The University of Newcastle

Callaghan NSW 2308

Australia

**Contact:**

Room ES208 ES building

E-mail:yuqing.lin@newcastle.edu.au

Phone: 49216076

**Employment and Education**

The University of Newcastle.

The University of Newcastle.

The University of Newcastle.

P.R.China.

**Research Interests:**

Network topology refers to the shape of a network, i.e. how different nodes in a network are connected to each other and how do they communicate. The primary function of a network is to exchange information among the nodes in the network and the network topology is one of the determining factors of the performance of a network. It is impractical to directly connect each pair of nodes in the network, also due to the hardware and software used in the network, the problem of designing network topologies is concerned with many constraints, for example, the limitation of the number of connections attached to every node, the limitation of the number of intermediate nodes on the communication route between any two given nodes.

It is customary to model a network topology by a graph, then these constrains correspond to various properties of the graph. For example, the above mentioned constrains correspond to the degree of a vertex and the distance between two nodes in graph theory terms. In this way, we transfer the problem of constructing an efficient network topology into the problem of constructing graphs with various desired properties.

Many interesting graphs have been proposed, such as Moore graph, Cages, Ex graph etc. For more details, see the Dynamic Survey for more details.

Graph labelling of a graph G is a mapping f that sends some set of graph elements to a set of numbers (usually positive or non-negative integers) such that the vertex weight and/or the edge weight of the induces graph has some special properties. Labelled graphs serve as useful models for a broad range of applications such as: coding theory, x-ray crystallography, radar, astronomy, circuit design, communication network addressing and data base management.

Over the past three decades many variations of labelling have evolved and many papers have been written on the subject of graph labelling, see the Dynamic Survey for more details.

Several factors have to be taken into account in the design of interconnection networks, such as

∗ Communication delays between processors must be short, the graph must have a small diameter or mean distance.

∗ The number of processors directly connected to a given processor is limited; the graph has a given maximum degree.

∗ The routing of the message must be simple and distributed if possible

∗ An interconnected network must be fault-tolerate, which means that the system still works in case of node or link failures. This means that the associated graph is sufficiently connected.

A graph or a digraph usually models the network. Thus a major factor of realizing highly reliable and efficient networks with a limited number of links is to find a graph with maximal connectivity for a given number of nodes and a given degree. The connectivity of graphs is a particularly intuitive area of graph theory and extends the concepts of cut node, bridge, and block. This concept represents the important property of computer and telecommunication network, also there is a rich body of the theorems concerning connectivity.

Not every network follows a well-defined regular structure. For example, the World Wide Web, the Internet, the cellular network, even the science collaboration network, do not have a regular structure. The dynamic type of networks has a large number of nodes, and the connections are very "random" in the sense that the connections follow various organizing principles or plans but do not have any globally unique rules for the whole network. In another words, the topology of the Dynamic Networks is not the product of a deliberate engineering attempt aimed at obtaining the best global solution possible, but rather it reflects in great part the choices and decisions made by individual organizations whose subnets form the Dynamic Networks. With the dynamic nature of this type of network, no one knows what exactly is the structure of any particular Dynamic Networks.

Developing tools and measurements to characterize this type of network has been attracting more and more attention. Additionally, how to improve the performance of Dynamic Networks also become a interesting problem, the methods to be discovered are also can be applied to various areas such as to improve the search engine mechanics and to construct more efficient Web Site etc.

**Recent submitted papers **

‘On the anti-Kekule number of fullerenes’, Yang Qin, Ye Dong, Zhang Heping and Lin Yuqing, submitted to * J.Math. Chem.*,

‘A note on even disjoint union of paths’, Baca Martin, Lin Yuqing, Muntaner-Batle Francesc A, submitted to *Utilitas
Math.*

‘On Superconnectivity of (4,g)-Cages’, Lin Yuqing, Qinglin Yu, Balbuena Camino, Marcote Xavier, Wu Yunjian and Lu Hongliang, submitted to *Graph and Combinatorics.*

** Recent Published Papers **, List maintained by the University of Newcastle

**Journal Article**

Baca Martin, Lin Yuqing, Muntaner-Batle Francesc A, ‘A note on even disjoint union of paths’, *AKCE International Journal of Graphs and Combinatorics*, **6** 41-45 (2009)

Lin Yuqing, Smyth Bill, Baskoro Edy Tri, ‘Guest editors’, *Journal of Combinatorial Mathematics and Combinatorial Computing*, **71** - (2009)

Baca Martin, Lin Yuqing, Muntaner-Batle Francesc A, ‘Normalized embedding of path-like trees’, *Utilitas Mathematica*, **78** 11-31 (2009)

Baca Martin, Lin Yuqing, Semanicova-Fenovcikova Andrea, ‘Note on super antimagicness of disconnected graphs’, *AKCE International Journal of Graphs and Combinatorics*, **6** 47-55 (2009)

Delorme Charles, Flandrin Evelyne, Lin Yuqing, Miller Mirka, Ryan Joseph Francis, ‘On extremal graphs with bounded girth’, *Electronic Notes in Discrete Mathematics*, **34** 653-657 (2009)

Lin Yuqing, Balbuena Camino, Miller Mirka, ‘On the number of components of (k, g)-cages after vertex deletion’, *Discrete Applied Mathematics*, **157** 1760-1765 (2009)

Ali Gohar, Baca Martin, Lin Yuqing, Semanicova-Fenovcikova Andrea, ‘Super-vertex-antimagic total labelings of disconnected graphs’, *Discrete Mathematics*, **309** 6048-6054 (2009)

Balbuena Camino, Tang Jianmin, Marshall Kim Louise, Lin Yuqing, ‘Superconnectivity of regular graphs with small diameter’, *Discrete Applied Mathematics*, **157** 1349-1353 (2009)

Balbuena Camino, Lin Yuqing, Miller Mirka, ‘Diameter-sufficient conditions for a graph to be super-restricted connected’, *Discrete Applied Mathematics*, **156** 2827-2834 (2008)

Tang Jianmin, Miller Mirka, Lin Yuqing, ‘HSAGA and its application for the construction of near-Moore digraphs’, *Journal of Discrete Algorithms*, **6** 73-84 (2008)

Lin Yuqing, Balbuena Camino, Marcote Xavier, Miller Mirka, ‘On the connectivity of (k, g)-cages of even girth’, *Discrete Mathematics*, **308** 3249-3256 (2008)

Balbuena C, Jiang T, Lin Yuqing, Marcote X, Miller M, ‘A lower bound on the order of regular graphs with given girth pair’, *Journal of Graph Theory*, **55** 153-163 (2007)

Baca M, Lin Yuqing, ‘Antimagic labelings of grids’, *Utilitas Mathematica*, **72** 65-75 (2007)

Baca M, Lin Yuqing, Miller M, Youssef M Z, ‘Edge-antimagic graphs’, *Discrete Mathematics*, **307** 1232-1244 (2007)

Baca M, Lin Yuqing, Muntaner-Batle F A, ‘Super edge-antimagic labelings of the path-like trees’, *Utilitas Mathematica*, **73** 117-128 (2007)

Lin Yuqing, Miller Mirka, Balbuena C, Marcote X, ‘All (k;g)-Cages Are Edge-Superconnected’, *Networks*, **47** 102-110 (2006)

Baca M, Lin Yuqing, Miller Mirka, Ryan Joseph Francis, ‘Antimagic labelings of Mobius grids’, *Ars Combinatoria*, **78** 3-13 (2006)

Tang Jianmin, Lin Yuqing, Milller Mirka, ‘Calculating the extremal number ex(v;{C3,C4,...,Cn})’, *Electronic Notes in Discrete Mathematics*, **27** 101-102 (2006)

Balbuena C, Barker E, Lin Yuqing, Miller M, Sugeng K, ‘Consecutive magic graphs’, *Discrete Mathematics*, **306** 1817-1829 (2006)

Lin Yuqing, Sugeng Kiki Ariyanti, ‘Face antimagic labelings of plane graphs P-a(b)’, *Ars Combinatoria*, **80** 259-273 (2006)

Sugeng K A, Miller M, Lin Yuqing, Baca M, ‘Face antimagic labelings of prisms’, *Utilitas Mathematica*, **71** 269-286 (2006)

Balbuena C, Barker E, Das K C, Lin Yuqing, Miller M, Ryan J, Slamin, Sugeng K, Tkac A, ‘On the degrees of a strongly vertex-magic graph’, *Discrete Mathematics*, **306** 539-551 (2006)

Lin Yuqing, Miller M, Rodger C, ‘All (k;g)-cages are k-edge-connected’, *Journal of Graph Theory*, **48** 219-227 (2005)

Lin Yuqing, Miller Mirka, Balbuena Camino, ‘Improved lower bound for the vertex connectivity of ([delta];g)-cages’, *Discrete Mathematics*, **299** 162-171 (2005)

Balbuena C, Barker E, Das K C, Lin Yuqing, Miller Mirka, Ryan J, Slamin, Sugeng K, Tkac M, ‘On The Degrees of A Strongly Vertex-Magic Graph’, *Discrete Mathematics*, **306** 539-551 (2005)

Lin Yuqing, Slamin, Martin Baca, Miller Mirka, ‘On d-antimagic labelings of prisms’, *ARS Combinatoria*, **72** 65-76 (2004)

Lin Yuqing, Slamin, Miller Mirka, ‘On d-antimagic labelings of antiprisms’, *Utilitas Mathematica*, **64** 213-220 (2003)

**Conference Publication**

Lin Yuqing, Ye Huilin, Li Bojun, ‘A new parameter for product configuration in software product lines’, *Proceedings: 2009 Second International Symposium on Knowledge Acquisition and Modeling KAM 2009*, Huazhong Normal University, China (2009)

Lin Yuqing, Ye Huilin, ‘Input data representation for self-organising map in software classification’, *Proceedings: 2009 Second International Symposium on Knowledge Acquisition and Modeling KAM 2009*, Huazhong Normal University, China (2009)

Lin Yuqing, Ye Huilin, Tang Jianmin, ‘Measurement of the complexity of variation points in software product lines’, *Proceedings 2009 WRI World Congress on Software Engineering*, Xiamen, China (2009)

Brankovic Ljiljana, Lin Yuqing, Smyth William F, ‘Conference editors’, *Proceedings of the International Workshop on Combinatorial Algorithms 2007*, Newcastle, NSW (2008)

Tang Jianmin, Lin Yuqing, Miller Mirka, ‘Construction of extremal graphs’, *IWOCA 2008: Proceedings of 19th International Workshop on Combinatorial Algorithms*, Nagoya, Japan (2008)

Lin Yuqing, ‘On super antimagic labeling of disconnected graphs’, *Proceedings of the Fourth International Workshop on Graph Labelings*, Harbin, China (2008)

Ye Huilin, Lin Yuqing, ‘A formal specification for product configuration in software product lines’, *Proceedings of the Nineteenth International Conference on Software Engineering & Knowledge Engineering (SEKE'2007)*, Boston, Massachusetts (2007)

Lin Yuqing, ‘A survey on the connectivity of cages and other related graphs’, *15th International Conference of Forum for Interdisciplinary Mathematics on Interdisciplinary Mathematical & Statistical Techniques. Abstracts*, Shanghai, China (2007)

Tang Jianmin, Balbuena Camino, Lin Yuqing, Miller Mirka, ‘An open problem: (4; g)-cages with odd g>5 are tightly superconnected’, *Theory of Computing*, Ballarat, VIC (2007)

Lin Yuqing, Tang J, Brankovic Ljiljana, Miller Mirka, ‘On graphs of maximum size with given girth’, *Proceedings of the Seventeenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2006)*, Uluru, NT (2006)

Lin Yuqing, Miller Mirka, ‘A Survey on the Connectivity of Cages’, *Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005) : September 18-21, 2005 Ballarat, Australia*, Ballarat, Vic. (2005)

Tang Jianmin, Miller Mirka, Lin Yuqing, ‘Hybrid Simulated Annealing and Genetic Algorithm for Degree/Diameter Problem’, *Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005) : September 18-21, 2005 Ballarat, Australia*, Ballarat, Vic. (2005)

Lin Yuqing, Ahmad Abeed, Mirka Miller, Kiki Sugeng, Martin Baca, ‘Further results on d-antimagic labelings of antiprisms’, *Proceedings from Fifteenth Australasian Workshop on Combinatorial Algorithms*, Ballina NSW, Aust (2004)