THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP
Let G be a finite group, H be a subgroup of G, and g be a fixed element of G. The relative g-noncommuting graph ?(g,H,G) of G is defined as a graph with the vertex set G, where two distinct vertices x and y are adjacent if [x, y] ?= g or [x, y] ?= g?1, and at least one of x or y belongs to H. Thi...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/73347 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G be a finite group, H be a subgroup of G, and g be a fixed element of G. The
relative g-noncommuting graph ?(g,H,G) of G is defined as a graph with the vertex
set G, where two distinct vertices x and y are adjacent if [x, y] ?= g or [x, y] ?= g?1,
and at least one of x or y belongs to H. This thesis will determine the degree of vertices
and the number of edges of the g-noncommuting relative graph, particularly
for the dihedral group (D2n). In this dihedral group, only two types of subgroups
will be discussed, namely H = ?a? and H = ?ajb? for some j = 0, 1, . . . , n ? 1.
Additionally, several topological indices of the relative g-noncommuting graph of
the dihedral group will be provided, such as the first Zagreb index, Wiener index,
Wiener-side index, hyper Wiener index, and Harary index. |
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