The thickness of amalgamations and Cartesian product of graphs | Zendy

Yichao Chen | Zendy; Yan Yang | Zendy

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The thickness of amalgamations and Cartesian product of graphs

Author(s) -

Yichao Chen,

Yan Yang

Publication year - 2016

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1942

Subject(s) - cartesian product , mathematics , combinatorics , product (mathematics) , cartesian coordinate system , discrete mathematics , geometry

The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n

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