Search results for "Highly irregular graph"

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Highly irregular graphs with extreme numbers of edges

1997

Abstract A simple connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we find: (1) the greatest number of edges of a highly irregular graph with n vertices, where n is an odd integer (for n even this number is given in [1]), (2) the smallest number of edges of a highly irregular graph of given order.

Discrete mathematicsPseudoforestHighly irregular graphEdge-graceful labelingTheoretical Computer ScienceHypercube graphCombinatoricsCycle graphDiscrete Mathematics and CombinatoricsPath graphMultiple edgesComplement graphMathematicsofComputing_DISCRETEMATHEMATICSMathematicsDiscrete Mathematics
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Degree sequences of highly irregular graphs

1997

AbstractWe call a simple graph highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we examine the degree sequences of highly irregular graphs. We give necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a highly irregular graph.

Discrete mathematicsCombinatoricsSequenceLoop (graph theory)Simple graphDegree (graph theory)Frequency partition of a graphHighly irregular graphBiregular graphDiscrete Mathematics and CombinatoricsTheoretical Computer ScienceMathematicsMathematicsofComputing_DISCRETEMATHEMATICSDiscrete Mathematics
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