# Registered Data

Contents

- 1 [CT005]
- 1.1 [02271] Enumerate All Routes on a Doughnut
- 1.2 [00039] Recent developments on energy of graphs
- 1.3 [00979] Optimal radio channel assignment to transmitters in a network by graph labeling approach
- 1.4 [00511] Metapopulation network models explain non-Poissonian statistics of intercontact times
- 1.5 [00199] Covering Array on Product of Hypergraphs

# [CT005]

## [02271] Enumerate All Routes on a Doughnut

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: We consider a following doughnut routing problem. Given a matching $M=(U \cap V,E)$ as a bipartite graph, two concentric circles, the cyclic ordering of the vertices in $U$ and $V$ , we wish to draw $M$ with the minimum number of edge crossings so that the vertices in $U ($resp. $V)$ are on the smaller $($resp. larger$)$ circle with the given cyclic ordering. We propose an enumerate algorithm for all optimal solutions of the problem.**Classification**:__05C38__**Author(s)**:**Yasuko Matsui**(Tokai University)- Shin-ichi Nakano (Gunma University)

## [00039] Recent developments on energy of graphs

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Let $G$ be a simple graph of order $n$ and with adjacency matrix $A$. If $\lambda_{1},\lambda_{2},\dots,\lambda_{n}$ are the eigenvalues of $A$, Gutman defined the energy of $G$ as $E(G)=\sum_{i=1}^{n}|\lambda_{i}|$. This definition was motivated by several earlier known results for the Huckel molecular orbital total π-electron energy and so is closely related to the concepts of theoretical chemistry. We present recent developments on graph energy.**Classification**:__05C50__,__05C90__**Author(s)**:**Shariefuddin Pirzada**(University of Kashmir)

## [00979] Optimal radio channel assignment to transmitters in a network by graph labeling approach

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: An optimal radio channel assignment to transmitters in a network is modelled by graph labeling approach. A radio labeling of a graph $G$ is a mapping $f : V(G) \rightarrow \{0,1,2,\ldots\}$ satisfying $|f(u)-f(v)| \geq diam(G)+1-d(u,v)$ for all $u,v \in V(G)$. The radio number $rn(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling $f$ with $\max\{f(v) : v \in V(G)\}=k$. We present our recent results on optimal radio labelings of graphs.**Classification**:__05C78__,__05C15__,__05C12__**Author(s)**:**Devsi Dudabhai Bantva**(Lukhdhirji Engineering College, Morbi)

## [00511] Metapopulation network models explain non-Poissonian statistics of intercontact times

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Intercontact times in empirical data obtained from humans and animals typically obey heavy-tailed distributions as opposed to exponential distributions that would correspond to Poisson processes. We show that this phenomenon is a mathematical property of a most basic metapopulation network model used in epidemiology and ecology modeling, in which individuals move from a patch to another according to the simple or other types of random walks. Our results hold true for any network structure.**Classification**:__05C82__,__60K20__**Author(s)**:- Elohim Fonseca dos Reis (State University of New York at Buffalo)
**Naoki Masuda**(State University of New York at Buffalo)

## [00199] Covering Array on Product of Hypergraphs

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Covering array ((CA)) on a hypergraph $H$ is a combinatorial object, used in interaction testing of a complex system modeled as $H$. It is a matrix and the number of rows in it, called size, indicates the required number of tests. Minimizing the size of (CA) is important in industrial applications. Given $H$, determining the optimal size is NP-hard. We present a polynomial-time approximation algorithm to construct $CA$ on 3-uniform hypergraphs.**Classification**:__05C85__,__05C90__**Author(s)**:**Yasmeen Akhtar**(Birla Institute of Technology and Science, Pilani-Goa Campus)- Soumen Maity ( Indian Institute of Science Education and Research, Pune)