On Invariants of Graphs with Applications to Knot Theory
نویسنده
چکیده
To each weighted graph F, two invariants, a polynomial Pf(x,y, z) and the signature rj(r), are defined. The various partial degress of Pr(x,y, z) and c(T) are expressed in terms of maximal spanning graphs of T. Furthermore, one unexpected property of Tutte's dichromate is proved. These results are applied to knots or links in S3 .
منابع مشابه
Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
In this paper, we first collect the earlier results about some graph operations and then we present applications of these results in working with chemical graphs.
متن کاملKnot Theory for Self-indexed Graphs
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure, an integral flow. We call a self-indexed graph with integral flow a comte. The analogy with links...
متن کاملHOMOLOGY OF i-CONNECTED GRAPHS AND INVARIANTS OF KNOTS, PLANE ARRANGEMENTS, ETC
We describe several objects and problems of homological combinatorics, arising naturally in the theory of discriminants and plane arrangements, in particular the homology groups of complexes of connected and two-connected graphs and hypergraphs. Knot-theoretical motivations and applications are indicated, as well as first results of related calculations of homology groups of spaces of knots and...
متن کاملInvariants of Composite Networks Arising as a Tensor Product
We show how the results of Brylawski and Oxley [4] on the Tutte polynomial of a tensor product of graphs may be generalized to colored graphs and the Tutte polynomials introduced by Bollobás and Riordan [1]. This is a generalization of our earlier work on signed graphs with applications to knot theory. Our result makes the calculation of certain invariants of many composite networks easier, pro...
متن کاملSplice Graphs and their Vertex-Degree-Based Invariants
Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
متن کامل