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On the Line Degree Splitting Graph of a Graph

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Abstract:

In this paper, we introduce the concept of the line degree splitting graph of a graph. We obtain some properties of this graph. We find the girth of the line degree splitting graphs. Further, we establish the characterization of graphs whose line degree splitting graphs are eulerian, complete bipartite graphs and complete graphs.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 18)
Pages:
1-10
Citation:
B. Basavanagoud and R. S. Kusugal, "On the Line Degree Splitting Graph of a Graph", Bulletin of Mathematical Sciences and Applications, Vol. 18, pp. 1-10, 2017
Online since:
May 2017
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References:

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[2] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, (1969).

[3] A. J. Hoffman, On the line-graph of the complete bipartite graph, Ann. Math. Statist. 35 (1964) 883-885.

DOI: https://doi.org/10.1214/aoms/1177703593

[4] V.R. Kulli, M.S. Biradar, The line-splitting graph of graph, Acta Ciencia Indica. 28(3) (2002) 317-322.

[5] J. Moon, On the line-graph of the complete bigraph, Ann. Math. Statist. 34 (1963) 664-667.

DOI: https://doi.org/10.1214/aoms/1177704179

[6] R. Ponraj, S. Somasundaram, On the degree splitting graph of a graph, Natl. Acad. Sci. Lett. 27(7-8) (2004) 275-278.

[7] S.S. Shrikhande, On a characterization of the triangular association scheme, Ann. Math. Statist. 30 (1959) 39-47.

[8] S. S. Shrikhande, The uniqueness of the L2 association scheme, Ann. Math. Statist. 30 (1959) 781-798.

DOI: https://doi.org/10.1214/aoms/1177706207
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