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[CT005]

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)

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)

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)

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)

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)