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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id-itb.:733472023-06-19T15:02:41ZTHE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP Ain Supu, Nur Indonesia Theses Relative g-noncommuting graph, dihedral group, vertex degree, topological indices. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/73347 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. text |
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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. |
| format |
Theses |
| author |
Ain Supu, Nur |
| spellingShingle |
Ain Supu, Nur THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP |
| author_facet |
Ain Supu, Nur |
| author_sort |
Ain Supu, Nur |
| title |
THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP |
| title_short |
THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP |
| title_full |
THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP |
| title_fullStr |
THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP |
| title_full_unstemmed |
THE VERTEX DEGREE OF RELATIVE G-NONCOMMUTING GRAPH OF THE DIHEDRAL GROUP |
| title_sort |
vertex degree of relative g-noncommuting graph of the dihedral group |
| url |
https://digilib.itb.ac.id/gdl/view/73347 |
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1822992971209900032 |