Journal of Mathematics and Mathematics Education (JMME)
Vol 14, No 1 (2024): Journal of Mathematics and Mathematics Education (JMME)

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

Ajeng Maula Azizin (Sebelas Maret University)



Article Info

Publish Date
01 Jun 2024

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

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Journal Info

Abbrev

jmme

Publisher

Subject

Education Mathematics

Description

Journal Mathematics and Mathematics Education (JMME) is a peer-refereed open-access journal which has been established for the dissemination of state-of-the-art knowledge in the field of mathematics and mathematics education. This journal was founded by the Magister of Mathematics Education, ...