Denote by B∗ n the set of all k∗-cycle resonant hexagonal chains with n hexagons. For any Bn ∈ B ∗ n , let m(Bn) and i(Bn) be the numbers of matchings (=the Hosoya index) and the number of independent sets (=the Merrifield-Simmons index) of Bn, respectively. In this paper, we give a characterization of the k∗-cycle resonant hexagonal chains, and show that for any Bn ∈ B ∗ n , m(Hn) ≤ m(Bn) and ...

UNLABELLED Alternaria is a ubiquitous fungal genus that includes saprobic, endophytic and pathogenic species associated with a wide variety of substrates. In recent years, DNA-based studies revealed multiple non-monophyletic genera within the Alternaria complex, and Alternaria species clades that do not always correlate to species-groups based on morphological characteristics. The Alternaria co...

Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truth-related paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his “Deflationary Truth and the Liar” (JPL 28:455–488, 1999) Keith Simmons argues that the two streams bear on one another in an important way...

In Ars Comb. 84 (2007), 85–96, Pedersen and Vestergaard posed the problem of determining a lower bound for the number of independent sets in a tree of fixed order and diameter d. Asymptotically, we give here a complete solution for trees of diameter d ≤ 5. The lower bound is 5 and we give the structure of the extremal trees. A generalization to connected graphs is stated.

In this paper we find trees with minimal and maximal MerrifieldSimmons index over the set Ω (n, 2) of all trees with n vertices and 2 branching vertices, and also over the subset Ω (n, 2) of all trees in Ω (n, 2) such that the branching vertices are connected by the path Pt.

Early life.—Emory was born 12 April 1920, in Hillsboro, Fountain County, Indiana, the son of Floyd and Estel May McAlister Simmons, the middle child of three girls and two boys. He was very fond of Minnie, his maternal grandmother, called ‘‘Dolly’’ by everyone, who lived with the family. The family moved to Crawfordsville, Indiana, before Emory entered school to a home whose former location is ...

The subliminal channel is one of the methods for hiding a message in other messages. Simmons has shown conjectures on the upper bound to the bandwidth of a subliminal channel. This paper proposes a new broad-band subliminal channel embedded in the ESIGN. The bandwidth of the proposed subliminal channel is wider than that of the previous one, and it exceeds the upper bound that Simmons has conje...