Abstract
For a finite group G, the intersection graph of G is the graph whose vertex set is the set of all proper non-trivial subgroups of G, where two distinct vertices are adjacent if their intersection is a non-trivial subgroup of G. In this article, we investigate the detour index, eccentric connectivity, and total eccentricity polynomials of the intersection graph of subgroups of the dihedral group for distinct primes . We also find the mean distance of the graph .
Highlights
The concept of intersection graph of subgroups of a finite group was defined and studied byCsa’ka’ny and Polla’k in 1969 [1]
The intersection graph of is an undirected simple graph whose vertex-set consists of all nontrivial proper subgroups of for which two distinct vertices H and K of are adjacent if ⋂ is a nontrivial subgroup of
This kind of graph has been studied by researchers; we refer the reader to see [2,3,4,5,6]
Summary
The concept of intersection graph of subgroups of a finite group was defined and studied by. Csa’ka’ny and Polla’k in 1969 [1] They found the clique number and degree of vertices of an intersection graph of subgroups of a dihedral group, quaternion group, and quasi-dihedral group. The intersection graph of is an undirected simple (without loops and multiple edges) graph whose vertex-set consists of all nontrivial proper subgroups of for which two distinct vertices H and K of are adjacent if ⋂ is a nontrivial subgroup of. This kind of graph has been studied by researchers; we refer the reader to see [2,3,4,5,6].
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