DOMINANCE NUMBER OF THE GRAPH RESULTING FROM COMB OPERATION BETWEEN COMPLETE GRAPH AND WHEEL GRAPH

Ajeng Maula Azizin

Abstract

Abstract: The purpose of this research is to know the graph of comb operation result between complete graph and wheel graph and the general formula of domination number of graph of comb operation result between complete graph and wheel graph. The research method used is a literature study by collecting various literature related to the problem under study. In graph theory, the domination number is the number of dominating vertices in a graph that can dominate the surrounding connected vertices, with the minimum number of dominating vertices of the surrounding connected vertices. Various types of graphs in domination numbers are growing, one of which is the domination number between graphs resulting from the comb operation of complete graphs and wheel graphs. The comb operation on complete graphs and wheel graphs denoted as  ⊳  is an operation performed by taking duplicates of  and |V()| duplicates of  and attaching vertex  on the i-th duplicate of  with the i-th vertex in the graph . The dominance number of the graph  ⊳  is divided into 4 cases, namely: domination number of graph ⊳  with m & n odd, domination number of graph ⊳  with m & n even, domination number of graphs ⊳  with m even & n odd and the domination number of graphs ⊳  with m odd & n even. General formula for the domination number of graphs resulting from the comb operation of complete graphs and wheel graphs  ⊳  is :

γ(⊳  =

Keywords: dominance number, comb operation, complete graph, wheel graph

Keywords

Keywords: dominance number, comb operation, complete graph, wheel graph

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References

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DOI: https://doi.org/10.20961/jmme.v14i1.79749

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