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2010•Unpublished venueRequires access

Research on the Girth of the BC Graph

Yanzhong Hu, Hao Li, Jinsong Zhou

Open publisher page 1 citations

Abstract

A Cubic graph is a 3-regular graph. The graph which is both a bipartite graph and a cubic graph is called the BC Graph. This paper deals with the existence and some properties of the BC graph, has proved that the girth concerning the graph which is characteristic of planar, bipartite and cubic properties, is four, and an original illustration about the BC graph with the girth of six is given. Finally, it introduces some well-recognised illustrations about the cubic graph of which the girth is greater than or equal to six.

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What this paper is about

A Cubic graph is a 3-regular graph. The graph which is both a bipartite graph and a cubic graph is called the BC Graph. This paper deals with the existence and some properties of the BC graph, has proved that the girth concerning the graph which is characteristic of planar, bipartite and cubic properties, is four, and an original illustration about the BC graph with the girth of six is given. Finally, it introduces some well-recognised illustrations about the cubic graph of which the girth is greater than or equal to six.

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Available abstract

A Cubic graph is a 3-regular graph. The graph which is both a bipartite graph and a cubic graph is called the BC Graph. This paper deals with the existence and some properties of the BC graph, has proved that the girth concerning the graph which is characteristic of planar, bipartite and cubic properties, is four, and an original illustration about the BC graph with the girth of six is given. Finally, it introduces some well-recognised illustrations about the cubic graph of which the girth is greater than or equal to six.

Key concepts: Cubic graph, Foster graph, Voltage graph, Combinatorics, Butterfly graph, Quartic graph, Mathematics, Graph power

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