Index graphs of finite permutation groups
نویسندگان
چکیده
Let <em>G</em> be a subgroup of <em>S</em><sub>n</sub>. For <em>x ∈ G</em>, the index <em>x</em> in is denoted by <em>ind x</em> minimal number 2-cycles needed to express as product. In this paper, we define new kind graph on <em>G</em>, namely and <em>Γ</em><sup>ind</sup><em>(G)</em>. Its vertex set all conjugacy classes two distinct vertices C</em><sub>x</sub> <em>y C</em><sub>y</sub> are adjacent if <em>Gcd(ind x, ind y) 6 ≠ 1</em>. We study some properties for symmetric groups <em>S</em><sub>n</sub>, alternating group <em>A</em><sub>n</sub>, cyclic <em>C</em><sub>n</sub>, dihedral <em>D</em><sub>2n</sub> generalized quaternain <em>Q</em><sub>4n</sub>. particular, interested connectedness them.
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ژورنال
عنوان ژورنال: Indonesian journal of combinatorics
سال: 2022
ISSN: ['2541-2205']
DOI: https://doi.org/10.19184/ijc.2022.6.2.2