A112921 -id:A112921 - cp's OEIS frontend

A112917 Number of nonisomorphic H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m

1, 1, 4, 6, 7, 13, 19, 31, 24, 76, 41, 77, 116, 116, 87, 226, 115, 307, 276, 308, 201, 671, 317, 523, 478, 786, 403, 1495

Offset: 3

Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005

An H-graph H(n:i,j;k,m) has 6n vertices arranged in six segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3,4,5 and y in the integers modulo n. The edges are v_{0,y}v_{1,y}, v_{0,y}v_{2,y}, v_{0,y}v_{3,y}, v_{1,y}v_{4,y}, v_{1,y}v_{5,y} (inner edges) and v_{2,y}v_{2,y+i}, v_{3,y}v_{3,y+j}, v_{4,y}v_{3,y+k}, v_{5,y}v_{5,y+m} (outer edges) where y=0,1,...,n-1 and subscript addition is performed modulo n.

			The only connected symmetric H-graphs are H(17:1,4;2,8) and H(34:1,13;9,15) which are also listed in Foster's Census.

I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.

J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129.

Cf. A112918, A112919, A112920, A112921, A107452.

A112922 Number of nonisomorphic connected Y-graphs Y(n:i,j,k) on 4n vertices (or nodes) for 1<=i,j,k

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 7, 8, 7, 19, 10, 16, 23, 20, 15, 33, 19, 43, 39, 37, 26, 73, 36, 52, 49, 75, 40, 127, 46, 78, 83, 87, 85, 149, 64, 109, 113, 163, 77, 227, 85, 167, 167, 158, 100, 266, 124, 222, 183, 229, 126

Offset: 3

Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005

A Y-graph Y(n:i,j,k) has 4n vertices arranged in four segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3 and y in the integers modulo n. The edges are v_{1,y}v_{1,y+i}, v_{2,y}v_{2,y+j}, v_{2,y}v_{2,y+k} and v_{0,y}v_{x,y}, where y=0,1,...,n-1 and x=1,2,3 and the subscript addition is performed modulo n. It is connected if and only if gcd(n,i,j,k) = 1.

			Y(7:1,2,3) is the Coxeter graph, the only symmetric (vertex- and edge-transitive) Y-graph of girth 7 or less.

I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.

J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129.

Cf. A112921, A112923, A112924.

A112923 Number of nonisomorphic connected bipartite Y-graphs Y(n:i,j,k) on 8n vertices (or nodes) for 1<=i,j,k<=n.

Original entry on oeis.org

1, 1, 2, 2, 5, 4, 5, 7, 9, 7, 14, 10, 15, 23, 15, 15, 27, 19, 28, 39, 29, 26, 45, 36, 39

Offset: 2

Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005

A Y-graph Y(n:i,j,k) has 4n vertices arranged in four segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3 and y in the integers modulo n. The edges are v_{1,y}v_{1,y+i}, v_{2,y}v_{2,y+j}, v_{2,y}v_{2,y+k} and v_{0,y}v_{x,y}, where y=0,1,...,n-1 and x=1,2,3 and the subscript addition is performed modulo n.

			Y(4:1,1,1) is the smallest bipartite Y-graph.
Y(14:1,3,5) is the smallest bipartite symmetric (vertex- and edge-transitive) Y-graph.

I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.

J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129.

Cf. A112921, A112922, A112924.

A112924 Number of nonisomorphic connected Y-graphs Y(n:i,j,k) with girth 6 on 4n vertices (or nodes) for 1<=i,j,k<=n.

Original entry on oeis.org

0, 0, 0, 1, 3, 2, 3, 2, 5, 3, 6, 6, 4, 4, 8, 12, 9, 4, 12, 10, 11, 19, 10, 12, 15, 12, 14, 22, 15, 12, 20, 16, 18, 31, 18, 18, 24, 16, 20, 50, 21, 20, 28, 22, 23, 50, 27, 24, 32, 24, 26

Offset: 3

Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005

A Y-graph Y(n:i,j,k) has 4n vertices arranged in four segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3 and y in the integers modulo n. The edges are v_{1,y}v_{1,y+i}, v_{2,y}v_{2,y+j}, v_{2,y}v_{2,y+k} and v_{0,y}v_{x,y}, where y=0,1,...,n-1 and x=1,2,3 and the subscript addition is performed modulo n.

			Y(6:1,1,1) is the smallest Y-graph with girth 6.

I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.

J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129.

Cf. A112921, A112922, A112923.

cp's OEIS Frontend

A112917 Number of nonisomorphic H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m

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A112922 Number of nonisomorphic connected Y-graphs Y(n:i,j,k) on 4n vertices (or nodes) for 1<=i,j,k

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A112923 Number of nonisomorphic connected bipartite Y-graphs Y(n:i,j,k) on 8n vertices (or nodes) for 1<=i,j,k<=n.

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A112924 Number of nonisomorphic connected Y-graphs Y(n:i,j,k) with girth 6 on 4n vertices (or nodes) for 1<=i,j,k<=n.

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