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Search: All articles in the CMB digital archive with keyword bipartite graph

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1. CMB 2016 (vol 59 pp. 705)

Chen, Yichao; Yin, Xuluo
The Thickness of the Cartesian Product of Two Graphs
The thickness of a graph $G$ is the minimum number of planar subgraphs whose union is $G.$ A $t$-minimal graph is a graph of thickness $t$ which contains no proper subgraph of thickness $t.$ In this paper, upper and lower bounds are obtained for the thickness, $t(G\Box H)$, of the Cartesian product of two graphs $G$ and $H$, in terms of the thickness $t(G)$ and $t(H)$. Furthermore, the thickness of the Cartesian product of two planar graphs and of a $t$-minimal graph and a planar graph are determined. By using a new planar decomposition of the complete bipartite graph $K_{4k,4k},$ the thickness of the Cartesian product of two complete bipartite graphs $K_{n,n}$ and $K_{n,n}$ is also given, for $n\neq 4k+1$.

Keywords:planar graph, thickness, Cartesian product, $t$-minimal graph, complete bipartite graph

2. CMB 2013 (vol 57 pp. 188)

Rad, Nader Jafari; Jafari, Sayyed Heidar
A Characterization of Bipartite Zero-divisor Graphs
In this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings $R$ with $1$, such that $R$ is finite or $|Nil(R)|\neq2$.

Keywords:zero-divisor graph, bipartite graph
Categories:13AXX, 05C25

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