a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

In this paper, the Hyper - Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].

We study state transfer in quantum walks on graphs relative to the adjacency matrix. Our motivation is to understand how the addition of pendant subgraphs affect state transfer. For two graphs G and H, the Frucht-Harary corona product G ◦H is obtained by taking |G| copies of the cone K1 + H and by identifying the conical vertices according to G. Our work explores conditions under which the coro...

let g and h be two graphs. the corona product g o h is obtained by taking one copy of gand |v(g)| copies of h; and by joining each vertex of the i-th copy of h to the i-th vertex of g,i = 1, 2, …, |v(g)|. in this paper, we compute pi and hyper–wiener indices of the coronaproduct of graphs.

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

The visible vibronic emission spectrum was recorded from the corona discharge of precursor 1,2,3,4tetramethylbenzene with a large amount of inert carrier gas helium using a pinhole-type glass nozzle coupled with corona excited supersonic expansion. The spectrum showed a series of vibronic bands in the D1 → D0 electronic transition of jet-cooled benzyl-type radicals formed from the precursor in ...

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

The total irregularity of a graph G is defined as irrt .G/ D 1 2 P u;v2V.G/ jdG.u/ dG.v/j, where dG.u/ denotes the degree of a vertex u 2 V.G/. In this paper we give (sharp) upper bounds on the total irregularity of graphs under several graph operations including join, lexicographic product, Cartesian product, strong product, direct product, corona product, disjunction and symmetric difference....