A property of the circuit characteristic polynomial

The intriguing class of altan‐molecules

“…Only 2 is an altan ‐molecule according to the original definition (namely, altan ‐[10]annulene). 3 is an altan according to the generalized definition of Gutman…”

“…Incidentally, it can be noticed that [2 n ,5]coronenes are altan ‐[2 n ]annulenes, a nomenclature that will be used in the following. The limitation to the whole set of C–H bonds on the outer perimeter for the aforementioned process, now called altanisation , has been removed by Gutman, who has proposed a generalized definition of altan ‐molecules, basically allowing the altanisation for subsets of C–H bonds …”

“…An extreme case of complication of the pattern has been reported for 7‐coronene 3 . This molecule is an altan according to the generalized definition of Gutman, but it is not an altan according to the original definition . 3 , like the first altan 2 , is formed by two annulenes, but here, the 4 n annulene, a [28]trannulene, is linked to a larger 4 n + 2 annulene, a [42]annulene, rather than to a smaller one.…”

“…Since their introduction, altan ‐molecules have attracted a considerable interest in the chemical and mathematical communities . Their topological definition has been extended, and limitations of the altanisation protocol have been investigated. No altan ‐molecule has been synthesized yet.…”

On the Narumi-Katayama Index of Composite Graphs

“…10 In the subsequent papers the more informative name "Narumi-Katayama index" was introduced and became established, so we use it in the present paper. In the beginning, the index attracted only a moderate attention, 4,6 but recently a number of papers appeared studying its various mathematical properties (such as the extremal graphs and values) 5 and its values over special classes of graphs. 12 Further, it also spawned various generalizations such as the degree product polynomial considered recently by Klein and Rosenfeld.…”