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Ars Combinatoria

  • Research article

Up-Embeddable Graphs Via the Degree-Sum of Nonadjacent Vertices: Non-Simple Graphs

Guanghua Dong1, Yanpei Liu2, Ning Wang3
1Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, P.R. China.
2Department of Mathematics, Beijing Jiaotong University, Betjing, 100044, P.R. China.
3Department of Information Science and Technology, Tianjin University of Finance and Economics, Tianjin, 200222, P.R. China.
  • Published: 30/04/2010

Abstract

A semi-double graph is a connected multi-graph such that each multi-edge consists of two edges. If there is at most one loop at each vertex of a semi-double graph, then this graph is called a single-petal graph. Via the degree-sum of nonadjacent vertices, the up-embeddability of semi-double graphs and single-petal graphs are discussed in this paper. And the results obtained in this paper can be extended to determine the up-embeddability of multi-graphs and pseudographs.

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Citation
Guanghua Dong, Yanpei Liu, Ning Wang. Up-Embeddable Graphs Via the Degree-Sum of Nonadjacent Vertices: Non-Simple Graphs[J], Ars Combinatoria, Volume 095. 129-141. .