نتایج جستجو برای: harary graph

تعداد نتایج: 198043  

Journal: :Graphs and Combinatorics 1992
Noga Alon Edward R. Scheinerman

Harary [8] calls a finite, simple graph G a sum graph if one can assign to each vi ∈ V (G) a label xi so that {vi, vj} ∈ E(G) iff xi + xj = xk for some k. We generalize this notion by replacing “xi + xj” with an arbitrary symmetric polynomial f(xi, xj). We show that for each f , not all graphs are “f -graphs”. Furthermore, we prove that for every f and every graph G we can transform G into an f...

Journal: :Discrete Mathematics & Theoretical Computer Science 2014
Olivier Baudon Julien Bensmail Éric Sopena

A graph G is arbitrarily partitionable (AP for short) if for every partition (n1, n2, ..., np) of |V (G)| there exists a partition (V1, V2, ..., Vp) of V (G) such that each Vi induces a connected subgraph of G with order ni. If, additionally, k of these subgraphs (k ≤ p) each contains an arbitrary vertex of G prescribed beforehand, then G is arbitrarily partitionable under k prescriptions (AP+k...

2012
Andrew Brooke-Taylor Damiano Testa

We study Fräıssé limits for certain Fräıssé classes over infinite relational languages that behave similarly to those for finite languages. These include the Fräıssé classes of finite simplicial complexes, finite hypergraphs, and Sperner families on finite sets. With a natural choice of measure we show that almost all countable structures whose finite substructures lie in such a class are isomo...

Fatemeh Shafiei

It is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. Quantitative structure – activity relationship (QSAR) studies and quantitative structure –property relationship (QSPR) studies are active areas of chemical research that focus on the nature ofthis dependency. Topological indices are the numerical value associated with chemical constitution...

Journal: :Discrete Mathematics 1998
Zhibo Chen

The idea of integral sum graphs was introduced by Harary (1994). A graph G is said to be an integral sum graph if its nodes can be given a labeling f with distinct integers, so that for any two distinct nodes u and v of G, uv is an edge of G if and only if f(u) + f(v) = f(w) for some node w in G. A tree is said to be a generalized star if it can be obtained from a star by extending each edge to...

The Harary index H can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. A generalization of the Harary index, denoted by Hk, is achieved by employing the Steiner-type distance between k-tuples of atoms. We show that the linear c...

2012
Simi Haber Saharon Shelah

We study zero-one laws for random graphs. We focus on the following question that was asked by many: Given a graph property P , is there a language of graphs able to express P while obeying the zeroone law? Our results show that on the one hand there is a (regular) language able to express connectivity and k-colorability for any constant k and still obey the zero-one law. On the other hand we s...

Journal: :Journal of Mathematics 2022

Consider λ to be a connected graph with vertex set id="M2"> V that may partitioned into any partition id="M3"> S . If each in id="M4"> has separate representation regard id="M5"> and is an ordered id="M6"> k partitio...

Journal: :J. Comb. Theory, Ser. B 1978
Ernest J. Cockayne Stephen T. Hedetniemi

This paper is motivated by Berge’s conjecture that every undirectefl regular graph, except the complement of a complete graph, has at least two disjoint maximal independent sets of vertices. By complementation this is equivalent to the conjecture that every incomplete regular graph has two or more disjoint cliques. In [l], we established this form of the conjecture for regular graphs of degree ...

Journal: :European Journal of Combinatorics 2023

The Ramsey number r(H) of a graph H is the minimum integer n such that any two-coloring edges complete Kn contains monochromatic copy H. While this definition only asks for single H, it often case every two-edge-coloring on vertices many copies over all two-colorings Kr(H) will be referred to as threshold multiplicity Addressing problem Harary and Prins, who were first systematically study quan...

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