Labeling graphs with two distance constraints

Product version of reciprocal degree distance of composite graphs

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.

A Note on Strongly Quotient Graphs

On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs

Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...

Constructing Graceful Graphs with Caterpillars

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...

Snakes and Caterpillars in Graceful Graphs

Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...