The Genera of Edge Amalgamations of Complete Bigraphs

Alpert, Seth A.

doi:10.2307/1996912

Transactions of the American Mathematical Society

1974

DOI: 10.2307/1996912

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The Genera of Edge Amalgamations of Complete Bigraphs

Seth A. Alpert¹

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1981

1989

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“…Amalgamations of complete graphs along five or fewer vertices were studied by Alpert [l], [2]. Also, amalgamations of cubes along subcubes was studied by Pica et al [ll].…”

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confidence: 97%

The Genus of Amalgamations

Archdeacon

1989

Annals of the New York Academy of Sciences

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“…Amalgamations of complete graphs along five or fewer vertices were studied by Alpert [l], [2]. Also, amalgamations of cubes along subcubes was studied by Pica et al [ll].…”

mentioning

confidence: 97%

The Genus of Amalgamations

Archdeacon

1989

Annals of the New York Academy of Sciences

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The genus of the 2‐amalgamations of graphs

Decker

Glover

Huneke

1981

Journal of Graph Theory

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A graph G is called the 2‐amalgamation of subgraphs G1 and G2 if G = G1 ∪ G2 and G1 ∩ G2 = {x, y}, 2 distinct points. in this case we write G = G1∪{x, y} G2. in this paper we show that the orientable genus, γ(G), satisfies the inequalities γ(G1) + γ(G2) − 1 ≤ γ(G1 ∪{x, y} G2) ≤ γ(G1) + γ(G2) + 1 and that this is the best possible result, i. e., the resulting three values for γ(G1 ∪{x, y} G2) which are possible can actually be realized by appropriate choices for G1 and G2.

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The Genera of Edge Amalgamations of Complete Bigraphs

Cited by 2 publications

References 2 publications

The Genus of Amalgamations

The Genus of Amalgamations

The genus of the 2‐amalgamations of graphs

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