Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

Let \(G=(V, E)\) be a simple graph and \(H\) subgraph of \(G\). Then \(G\) admits an \(H\)-covering, if every edge in \(E(G)\) belongs to at least one that is isomorphic \(H\). An \((a,d)-H\)-antimagic total labeling bijection \(f:V(G)\cup E(G)\rightarrow \{1, 2, 3,\dots, |V(G)| + |E(G)|\}\) such for all subgraphs \(H'\) \(H\), the weights \(w(H') =\sum_{v\in V(H')} f (v) \sum_{e\in E(H')} (e)\...

‎The largest class of hyperstructures is the one which satisfies the weak properties; these are called $H_{v}$-structures‎. ‎In this paper we introduce a special product of elements in $H_{v}$-group $H$ and define a new class of $H_{v}$-groups called strongly $H_{v}$-groups‎. ‎Then we show that in strongly $H_{v}$-groups $beta=beta^{ast}$‎. ‎Also we express $theta$-hyperoperation and investigat...

Let $H=H(V,E)$ be a non-trivial simple connected graph with edge and vertex set $E(H)$ $V(H)$, respectively. A subset $\mathbb{D}\subset V(H)$ distinct vertices is said to resolving in $H$ if for each pair of $p$ $q$ we have $d(p,u)\neq d(q,u)$ some $u\in H$. minimum possible metric basis $H$. The cardinality called the dimension $H$, denoted by $\dim_{v}(H)$. In this paper, prove that constant...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...

Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index ...