Search results for "05c76"

showing 4 items of 4 documents

About Graph Complements

2020

Summary This article formalizes different variants of the complement graph in the Mizar system [3], based on the formalization of graphs in [6].

Discrete mathematicsComputational Mathematicsgraph complementApplied MathematicsQA1-93905c76Graph (abstract data type)loop68v20MathematicsComplement graphMathematicsofComputing_DISCRETEMATHEMATICSMathematicsFormalized Mathematics
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About Graph Unions and Intersections

2020

Summary In this article the union and intersection of a set of graphs are formalized in the Mizar system [5], based on the formalization of graphs in [7].

Discrete mathematicsgraph theoryApplied Mathematics020207 software engineeringgraph intersection0102 computer and information sciences02 engineering and technology68v20Computer Science::Digital Libraries01 natural sciencesComputational Mathematicsgraph union010201 computation theory & mathematicsComputer Science::Mathematical SoftwareQA1-9390202 electrical engineering electronic engineering information engineering05c76Graph (abstract data type)MathematicsMathematicsofComputing_DISCRETEMATHEMATICSMathematicsFormalized Mathematics
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About Supergraphs. Part III

2019

Summary The previous articles [5] and [6] introduced formalizations of the step-by-step operations we use to construct finite graphs by hand. That implicitly showed that any finite graph can be constructed from the trivial edgeless graph K 1 by applying a finite sequence of these basic operations. In this article that claim is proven explicitly with Mizar[4].

EpigraphTheoretical computer scienceApplied Mathematics68t99Part iiiComputational Mathematics03b35construction of finite graphsQA1-93905c76Graph operationssupergraphgraph operationsMathematicsMathematicsFormalized Mathematics
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Underlying Simple Graphs

2019

Summary In this article the notion of the underlying simple graph of a graph (as defined in [8]) is formalized in the Mizar system [5], along with some convenient variants. The property of a graph to be without decorators (as introduced in [7]) is formalized as well to serve as the base of graph enumerations in the future.

Theoretical computer scienceApplied Mathematics020207 software engineering0102 computer and information sciences02 engineering and technology68t9901 natural sciencesComputational Mathematics03b35010201 computation theory & mathematicsSimple (abstract algebra)underlying simple graphQA1-9390202 electrical engineering electronic engineering information engineering05c76Graph operationsgraph operationsMathematicsMathematicsofComputing_DISCRETEMATHEMATICSMathematicsFormalized Mathematics
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