An independent set in a graph G is a set of pairwise non-adjacent vertices, and the independence number α(G) is the cardinality of a maximum independent set. The independence polynomial of G is I(G; x) = s0 + s1x+ s2x 2 + ...+ sαx , α = α(G), where sk equals the number of independent sets of size k in G (Gutman and Harary, 1983). If si = sα−i, 0 ≤ i ≤ α/2 , then I(G; x) is called palindromic. I...

T issue’s “From the Editors” column is coauthored with all the associate editors, to emphasize their major role in the leadership of the journal. We first review this year’s operations and thank our editorial board and referees. Our first article, by David J. Johnstone, Victor Richmond R. Jose, and Robert L. Winkler, presents “Tailored Scoring Rules for Probabilities,” which take into account t...

A stable set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is I(G;x) = s0+s1x+s2x 2 +...+sαx α , where α = α(G) is the cardinality of a maximum stable of G, while sk equals the number of stable sets of size k in G (Gutman and Harary, 1983). Hamidoune, 1990, showed that for every claw-free graph G (i.e., a graph having no induced subgraph isomorphic to...

The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of independent bets available to an investor. Conventionally applications using breadth frequently assume only the number of separate bets. There may be a large discrepancy between these t...

Let S(Gσ) be the skew-adjacency matrix of an oriented graph Gσ . The skew energy of Gσ is the sum of all singular values of its skew-adjacency matrix S(Gσ). This paper first establishes an integral formula for the skew energy of an oriented graph. Then, it determines all oriented graphs with minimal skew energy among all connected oriented graphs on n vertices with m (n ≤ m < 2(n− 2)) arcs, whi...

In the early studies on atromid, which is ethyl p-chlorophenoxyisobutyric acid (clofibrate or C.P.I.B.) with androsterone, Thorp (1962) reported that, in monkeys, this preparation increased uric acid excretion in addition to lowering plasma lipids. Also Oliver (1962) reported that atromid lowered serum uric acid levels in patients with ischaemic heart disease. We therefore investigated its poss...

Although the literature on the permeability of the placenta to many substances either of a metabolic or foreign origin is extensive, there is a paucity of data on comparisons of maternal and infant total base. In 1920 Stander and Tyler (1) reported identical values for the ash of maternal and fetal plasma, while Levy-Solal, Dalsace, and Gutman (2) in 1934 reported the maternal and fetal plasma ...

Gout complicating cyanotic congenital heart disease is infrequently recognized. Its occurrence in blood dyscrasias associated with hyperuricamia is well documented (Gliickmann, 1910; Weber, 1934; Barr et al., 1950; Hickling, 1953). In polycythemia rubra vera, gout occurs in 5 to 9 per cent of patients (Tinney et al., 1945; Videbaek, 1950; Lawrence, 1955) and the complication has been referred t...

The trace norm ‖G‖∗ of a graph G is the sum of its singular values, i.e., the absolute values of its eigenvalues. The norm ‖G‖∗ has been intensively studied under the name of graph energy, a concept introduced by Gutman in 1978. This note focuses on the maximum trace norm of r-partite graphs, which for r > 2 raises some unusual problems. It is shown that, if G is an r-partite graph of order n, ...

Introduction Facial myokymia is an unusual form of involuntary movement of the facial musculature which is characterized by spontaneous undulating waves of contracting muscle fibres spreading across the face. In a recent review, Gutman, Thompson & Martin (1969) were able to find forty cases reported in the world literature and added two of their own. Of these cases, in twenty-three the diagnosi...