Advances and Applications in Discrete Mathematics
Volume 16, Issue 1, Pages 13 - 30
(July 2015) http://dx.doi.org/10.17654/AADMJul2015_013_030 |
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NONEXISTENCE OF CUBIC DDI GRAPHS OF ORDER 16 WITH DIAMETERS 4, 5, 6
Medha Itagi Huilgol and M. Rajeshwari
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Abstract: The eccentricity of a vertex u is the maximum distance of u to any other vertex of G. The distance degree sequence (dds) of a vertex v in a graph is a list of the number of vertices at distance in that order, where denotes the eccentricity of v in G. Thus, the sequence is the distance degree sequence of the vertex in G, where denotes the number of vertices at distance j from A graph is distance degree regular (DDR) graph if all the vertices have the same distance degree sequence. A graph is distance degree injective (DDI) graph if no two vertices have the same distance degree sequence. In this paper, we prove that there does not exist cubic DDI graphs of order 16 with diameters 4, 5, 6. |
Keywords and phrases: eccentric vertex, distance degree sequence, DDR graph, DDI graph. |
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