In this paper, we study several distance-based entropy measures on fullerene graphs. These include the topological information content of a graph I a ( G ) , a degree-based entropy measure, the eccentric-entropy I f σ ( G ) , the Hosoya entropy H ( G ) and, finally, the radial centric information entropy H e c c . We compare these measures on two infinite classes of fullerene graphs denoted by A 12 n + 4 and B 12 n + 6 . We have chosen these measures as they are easily computable and capture meaningful graph properties. To demonstrate the utility of these measures, we investigate the Pearson correlation between them on the fullerene graphs.
Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with pentagonal and hexagonal faces is called as a classical fullerene. The aim of this paper is to survey some results about the symmetry group of cubic polyhedral graphs. We show that the order of symmetry group of such graphs divides 240.
Let $G$ be a finite group. The set $D\subseteq G$with $|D|=k$ is called a $(n,k,\lambda,\mu)$-partial difference set(PDS) in $G$ if the differences $d_1d_2 ^{-1}, d_2,d_2\in D, d_1\neq d_2$, represent each non-identity element in $D$ exactly $\lambda$ times and each non-identity element in $G-\{D\}$ exactly $\mu$ times.In the present paper, we determine for which group $G\in \{D_{2n},T_{4n},U_{6n},V_{8n}\}$ the derangement set is a PDS. We also prove that the derangement set of a Frobenius group is a PDS.
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