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...

A linear forest is the union of a set of vertex disjoint paths. Akiyama, Exoo and Harary and independently Hilton have conjectured that the edges of every graph of maximum degree ∆ can be covered by d∆+1 2 e linear forests. We show that almost every graph can be covered with this number of linear forests. 1 Linear Forests, Directed Cycles, and the Probabilistic Method A linear forest is the uni...

Let G1 and G2 be disjoint copies of a graph G, and let f : V (G1) → V (G2) be a function. Then a functigraph C(G, f) = (V,E) has the vertex set V = V (G1) ∪ V (G2) and the edge set E = E(G1) ∪ E(G2) ∪ {uv | u ∈ V (G1), v ∈ V (G2), v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study ...

Graf koprima pada grup bilangan bulat modulo memiliki banyak aplikasi penting dalam matematika diskrit dan kriptografi. Indeks Harary dari graf sangat berguna ilmu komputer, terutama perhitungan properti aljabarik, topologi, struktur graf. Pada artikel ini didapatkan Hararay untuk yang berorde perpangkatan prima, yakni kuadrat jumlah anggota dikurangi satu.

The concept of continuous monotonic decomposition (CMD) was INTRODUCTION By a graph we mean a finite undirected graph without loops or multiple edges. Terms not defined here are used in the sense of Harary [1].

We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs. We also give an alternative proof of an extension to locally finite graphs of the result of Chartrand and Harary that a finite graph not containing K4 or K2,3 as a minor is Hamiltonian if and only if it is 2-connected. We show furth...

The aim of this note is to establish new spectral bounds for the harmonic matrix. The Harary matrix of given a connected graph G of order n, say RD(G), is an n-by-n symmetric matrix, such that (RD(G))ij =  1 dij , if i < j, 0 , if i = j, where dij denotes the distance between the vertices i and j [10, 11]. This matrix (originally known as reciprocal distance matrix [11]) is particulary well-k...

The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indic...

We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, The Netherlands, UK, USA. For each geographical entity we represented major urban areas by oat flakes and ino...