3,842 research outputs found
Signed total double Roman dominatıon numbers in digraphs
Let D = (V, A) be a finite simple digraph. A signed total double Roman dominating function (STDRD-function) on the digraph D is a function f : V (D) â {â1, 1, 2, 3} satisfying the following conditions: (i) P xâNâ(v) f(x) â„ 1 for each v â V (D), where Nâ(v) consist of all in-neighbors of v, and (ii) if f(v) = â1, then the vertex v must have at least two in-neighbors assigned 2 under f or one in-neighbor assigned 3 under f, while if f(v) = 1, then the vertex v must have at least one in-neighbor assigned 2 or 3 under f. The weight of a STDRD-function f is the value P xâV (D) f(x). The signed total double Roman domination number (STDRD-number) ÎłtsdR(D) of a digraph D is the minimum weight of a STDRD-function on D. In this paper we study the STDRD-number of digraphs, and we present lower and upper bounds for ÎłtsdR(D) in terms of the order, maximum degree and chromatic number of a digraph. In addition, we determine the STDRD-number of some classes of digraphs.Publisher's Versio
Weighted interlace polynomials
The interlace polynomials introduced by Arratia, Bollobas and Sorkin extend
to invariants of graphs with vertex weights, and these weighted interlace
polynomials have several novel properties. One novel property is a version of
the fundamental three-term formula
q(G)=q(G-a)+q(G^{ab}-b)+((x-1)^{2}-1)q(G^{ab}-a-b) that lacks the last term. It
follows that interlace polynomial computations can be represented by binary
trees rather than mixed binary-ternary trees. Binary computation trees provide
a description of that is analogous to the activities description of the
Tutte polynomial. If is a tree or forest then these "algorithmic
activities" are associated with a certain kind of independent set in . Three
other novel properties are weighted pendant-twin reductions, which involve
removing certain kinds of vertices from a graph and adjusting the weights of
the remaining vertices in such a way that the interlace polynomials are
unchanged. These reductions allow for smaller computation trees as they
eliminate some branches. If a graph can be completely analyzed using
pendant-twin reductions then its interlace polynomial can be calculated in
polynomial time. An intuitively pleasing property is that graphs which can be
constructed through graph substitutions have vertex-weighted interlace
polynomials which can be obtained through algebraic substitutions.Comment: 11 pages (v1); 20 pages (v2); 27 pages (v3); 26 pages (v4). Further
changes may be made before publication in Combinatorics, Probability and
Computin
Size and timing of profits for insurance companies: Cost assignment for products with multiple deliveries
Profit;Insurance Companies;business economics
Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)
International audienceOriginating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice.This international conference âAlgebras, graphs and ordered setâ (ALGOS) brings together specialists in the theory of graphs, relational structures and ordered sets, topics that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for mathematicians and computer scientists to meet, to present their latest results, and to discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects.The first edition of ALgebras, Graphs and Ordered Sets (ALGOS 2020) has a particular motivation, namely, an opportunity to honour Maurice Pouzet on his 75th birthday! For this reason, we have particularly welcomed submissions in areas related to Mauriceâs many scientific interests:âą Lattices and ordered setsâą Combinatorics and graph theoryâą Set theory and theory of relationsâą Universal algebra and multiple valued logicâą Applications: formal calculus, knowledge discovery, biomedical sciences, decision aid and social choice, security, social networks, web semantics..
The Pacifican September 12, 2013
https://scholarlycommons.pacific.edu/pacifican/1048/thumbnail.jp
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