let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

We say that a simple graph G is Seidel integral if its spectrum consists entirely of integers. In this work we establish characterization graphs which belong to the class ?Ka ? ?Kb,b, where mG denotes m-fold union G.

The problem of computing a maximum a posteriori (MAP) configuration is a central computational challenge associated with Markov random fields. A line of work has focused on “tree-based” linear programming (LP) relaxations for the MAP problem. This paper develops a family of super-linearly convergent algorithms for solving these LPs, based on proximal minimization schemes using Bregman divergenc...

In this paper the current distribution is calculated for a microstrip line in the presence of a neighboring strip. The electric field is calculated and the characteristic impedance of the slotted ndcrostrip line is determined. A graph of characteristic impedance is given for odd and even excitations. The calculations are carried out by setting up a singular integral equation which is solved usi...

Let D be the diameter of a graph G and let λ1 be the largest eigenvalue of its (0,1)adjacency matrix. We give a proof of the fact that there are exactly 69 non-trivial connected graphs with (D + 1)λ1 9. These 69 graphs all have up to 10 vertices and were recently found to be suitable models for small multiprocessor interconnection networks. We also examine the suitability of integral graphs to ...

In this white paper we report the work that was done on the problem of generation combinatorial structures with some rare invariant properties. These combinatorial structures are connected integral graphs. All (588) of such graphs of order 1 ≤ n ≤ 12 are known. The main goal of this work was to reduce the time of generation by distributing graph generators over hosts in PRACE-RI, and to reduce ...

We say that a simple graph G is Seidel integral if its spectrum consists entirely of integers. If ?Ka,a ? ?Kb,b integral, we show it belongs the class graphs [kt/? x0 + mt/?z]Ka,a y0 a/?z]nKb,b, where (i) = (t+?n)k+?m and b ?m; (ii) t, k, ?,m, n N such (m, n) 1, (n, t) 1 (?, 1; (iii) (a,mt) | kt; (iv) (x0, y0) particular solution linear Diophantine equation ax (mt)y (v) z z0 least integer (kt/?...

We characterize the family of connected subgraphs in terms of linear matrix inequalities (LMI) with additional integrality constraints. We then show that convex relaxations of the integral LMI lead to parameterization of all weighted connected subgraphs. These developments allow for optimizing arbitrary graph functionals under connectivity constraints. For concreteness we consider the connected...

This article raises questions about the meaning of “meaning,” which often is understood in terms of the referent or interpretant (sense) of mathematical signs. In this study, which uses data from an interview study with scientists who were asked to read graphs from their own work, a different approach is proposed with the intent to contribute toward a more appropriate theory of meaning. I argue...