Line graph - Revision history

Vipul at 16:00, 29 May 2012

2012-05-29T16:00:41Z

← Older revision		Revision as of 16:00, 29 May 2012
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	==Definition==		==Definition==

	Suppose <math>G</math> is an [[undirected graph]]. The '''line graph'''of <math>G</math>, denoted <math>L(G)</math>, is defined as follows:		Suppose <math>G</math> is an [[undirected graph]]. The '''line graph''' of <math>G</math>, denoted <math>L(G)</math>, is defined as follows:

	# The vertex set of <math>L(G)</matH> is defined as the edge set of <math>G</math>.		# The vertex set of <math>L(G)</matH> is defined as the edge set of <math>G</math>.
	# The edges of <math>L(G)</math> are defined as follows: two vertices of <math>L(G)</math> are adjacent if and only if, when viewed as edges of <math>G</math>, they share a common vertex.		# The edges of <math>L(G)</math> are defined as follows: two vertices of <math>L(G)</math> are adjacent if and only if, when viewed as edges of <math>G</math>, they share a common vertex.

Vipul at 15:59, 29 May 2012

2012-05-29T15:59:59Z

← Older revision		Revision as of 15:59, 29 May 2012
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			{{undirected graph operation}}

	==Name==		==Name==

Vipul at 18:49, 28 May 2012

2012-05-28T18:49:41Z

← Older revision		Revision as of 18:49, 28 May 2012
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	The construction outlined here goes by the name of the '''line graph'''. Alternate names are the '''theta-obrazom''', the '''covering graph''', the '''derivative''', the '''edge-to-vertex dual''', the '''conjugate''', and the '''representative graph''', as well as the '''edge graph''', the '''interchange graph''', the '''adjoint graph''', and the '''derived graph'''.		The construction outlined here goes by the name of the '''line graph'''. Alternate names are the '''theta-obrazom''', the '''covering graph''', the '''derivative''', the '''edge-to-vertex dual''', the '''conjugate''', and the '''representative graph''', as well as the '''edge graph''', the '''interchange graph''', the '''adjoint graph''', and the '''derived graph'''.

			==Definition==

			Suppose <math>G</math> is an [[undirected graph]]. The '''line graph'''of <math>G</math>, denoted <math>L(G)</math>, is defined as follows:

			# The vertex set of <math>L(G)</matH> is defined as the edge set of <math>G</math>.
			# The edges of <math>L(G)</math> are defined as follows: two vertices of <math>L(G)</math> are adjacent if and only if, when viewed as edges of <math>G</math>, they share a common vertex.

Vipul: Created page with "==Name== The construction outlined here goes by the name of the '''line graph'''. Alternate names are the '''theta-obrazom''', the '''covering graph''', the '''derivative''',..."

2012-05-28T18:47:52Z

Created page with "==Name== The construction outlined here goes by the name of the '''line graph'''. Alternate names are the '''theta-obrazom''', the '''covering graph''', the '''derivative''',..."

New page

==Name==

The construction outlined here goes by the name of the '''line graph'''. Alternate names are the '''theta-obrazom''', the '''covering graph''', the '''derivative''', the '''edge-to-vertex dual''', the '''conjugate''', and the '''representative graph''', as well as the '''edge graph''', the '''interchange graph''', the '''adjoint graph''', and the '''derived graph'''.