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Article
Wielandt Subgroups of Certain Finite Groups
The Wielandt subgroup of a finite group G is defined as w(G) = ∩H◁◁G NG(H). In this paper, this subgroup is computed for certain finite groups.
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Article
On the Number of Heisenberg Characters of Finite Groups
An irreducible character χ of a finite group G is called a Heisenberg character if Kerχ ⊇ [G, [G,G]]. In this paper, we prove that the group G has exactly r, r ≤ 3, Heisenberg characters if and only if |G/G′| = r
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Article
On a Special Quotient of the Generating Graph of a Finite Group
Suppose G is a finite group with identity element 1. The generating graph \(\Gamma (G)\) ...
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Article
First degree-based entropy of graphs
The first degree-based entropy of a connected graph G is defined as: $$I_1(G)=\log (\sum _{v_i\in V(G)}\deg (v_i))-\sum _{v_j\in V(G)}...
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Article
Topological efficiency under graph operations
In this paper we present explicit formulas for computing the topological efficiency index of the most important graph operations such as the Cartesian product, composition, corona, join and hierarchical produc...
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Article
Maximum values of atom–bond connectivity index in the class of tricyclic graphs
The atom–bond connectivity index of a graph \(G\) G
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Chapter
Topological Indices of 3-Generalized Fullerenes
A molecular graph G is said to be three connected if there does not exist a two-element set of vertices whose removal disconnects the graph. A three-connected cubic planar graph G = (V;E) is called m-generalized ...
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Article
The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups
A logarithmic signature for a finite group G is a sequence [A 1,⋯ ,A s ] of subsets of G such that every element g∈G can be uniqu...
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Article
The Undirected Power Graph of a Finite Group
The power graph \({\fancyscript{P}}(G)\) P ...
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Article
Tetracyclic graphs with extremal values of Randić index
Let \(G\) G be ...
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Article
Atom–bond connectivity index of quasi-tree graphs
The atom–bond connectivity index is a useful graph invariant suitable for stability of alkanes and the strain energy of cycloalkanes. In this paper, the first, second and third maximum of this topological inde...
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Article
Maximum values of atom–bond connectivity index in the class of tetracyclic graphs
In this paper, the first and second maximum values of the atom–bond connectivity index in the class of all n-vertex tetracyclic graphs are presented.
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Article
A note on normalized Laplacian energy of graphs
Themain goal of this paper is to obtain some bounds for the normalized Laplacian energy of a connected graph. The normalized Laplacian energy of the line and para-line graphs of a graph are investigated. The r...
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Article
Applications of the generalized hierarchical product of graphs in computing the vertex and edge PI indices of chemical graphs
The aim of this paper is to present exact formulas for the vertex and edge PI indices of the generalized hierarchical product of graphs. As a consequence of our results, these indices were computed for some ch...
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Article
Remarks on the Wiener index of unicyclic graphs
Unicyclic graphs are connected graphs with the same number of vertices and edges. Tang and Deng (J. Math. Chem. 43:60–74, 2008) considered the problem of classification of all unicyclic graphs with the first thre...
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Chapter
Mathematics of D5 Network
Diamond D5 is the generic name proposed by Diudea for hyperdiamonds constructed mostly from pentagons and hexagons. There are known several allotropes of D5; within this chapter only the clathrate II structure (t...
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Article
Full Non-rigid Group of Sponge and Pina
The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers and Villa computed the r-NRG of the triple equivalen...
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Article
Generalized latin square
LetX be a n-set and letA = [aij] be an xn matrix for whichaij ⊆X, for 1 ≤i, j ≤n. A is called a generalized Latin square onX, if the following conditions is satisfied:
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Article
Computing Orbits of the Automorphism Group of the Subsequence Poset B m,n
Let B m,n denote the set of all words obtained from the cyclic word of length n on an alphabet of m letters in by deleting on all possible ways and their natura...
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Article
nX-complementary generations of the Fischer group Fi 23
Let G be a finite group andnX a conjugacy class of elements of order n inG. G is callednX—complementary generated if, for everyx ∈ G−{1}, there is ay ∈nX such thatG = 〈hx,y〉.
