A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

let $g$ be a connected graph. the multiplicative zagreb eccentricity indices of $g$ are defined respectively as ${bf pi}_1^*(g)=prod_{vin v(g)}varepsilon_g^2(v)$ and ${bf pi}_2^*(g)=prod_{uvin e(g)}varepsilon_g(u)varepsilon_g(v)$, where $varepsilon_g(v)$ is the eccentricity of vertex $v$ in graph $g$ and $varepsilon_g^2(v)=(varepsilon_g(v))^2$. in this paper, we present some bounds of the multi...


 Let G be a connected graph. A set S of vertices in is 2-resolving hop dominating if and for every vertex x ∈ V (G)\S there exists y such that dG(x, y) = 2. The minimum cardinality called the domination number denoted by γ2Rh(G). This study aims to combine concept with sets graphs. main results generated this include characterization join, corona lexicographic product two graphs, as well ...

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product graphs and compute the Y new related to join graphs.

For an ordered set { } k w w w W , , , 2 1  = of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v/W) = (d(v, w1), d(v, w2), ..., d(v, wk)), where d(x, y)representsthe distance between the vertices x and y. A resolving set of minimum cardinality is called a minimum resolving set or abasis and the cardinality of a basis for G ...

the wiener index is a graph invariant that has found extensive application in chemistry. inaddition to that a generating function, which was called the wiener polynomial, who’sderivate is a q-analog of the wiener index was defined. in an article, sagan, yeh and zhang in[the wiener polynomial of a graph, int. j. quantun chem., 60 (1996), 959969] attainedwhat graph operations do to the wiener po...