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...

Abstract—In graph theory, different types of products of two graphs had been studied, e.g., Cartesian product, Tensor product, Strong product, etc. In this paper we generalize the concept of Cartesian product of graphs.We define 2 Cartesian product and more generally r Cartesian product of two graphs. We study these product mainly for path graphs. We also discuss connectedness of the new graph.

For any integer $k\geq 3$ , we define sunlet graph of order $2k$, denoted by $L_{2k}$, as the consisting a cycle length $k$ together with pendant vertices, each adjacent to exactly one vertex cycle. In this paper, give necessary and sufficient conditions for existence $L_{8}$-decomposition tensor product wreath complete graphs.

Abstract A strong edge coloring of a graph G is proper such that every color class an induced matching. The minimum number colors required termed the chromatic index. In this paper we determine exact value index all unitary Cayley graphs. Our investigations reveal underlying product structure from which graphs emerge. We then go on to give tight bounds for Cartesian two trees, including formula...

The tensor product, also called direct, categorical, or Kronecker product of graphs, is one of the least-understood graph products. In this paper we determine partial answers to the question given in the title, thereby significantly extending results of Broere and Hattingh (see [2]). We characterize completely those pairs of complete graphs whose tensor products are circulant. We establish that...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...