Distance Labeling for Permutation Graphs

Approximate Distance Labeling Schemes

We consider the problem of labeling the nodes of an n-node graph G with short labels in such a way that the distance between any two nodes u, v of G can be approximated efficiently (in constant time) by merely inspecting the labels of u and v, without using any other information. We develop such constant approximate distance labeling schemes for the classes of trees, bounded treewidth graphs, p...

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 the tenacity of cycle permutation graph

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

Localized and Compact Data-Structure for Comparability Graphs

We show that every comparability graph of any two-dimensional poset over n elements (a.k.a. permutation graph) can be preprocessed in O(n) time, if two linear extensions of the poset are given, to produce an O(n) space data-structure supporting distance queries in constant time. The data-structure is localized and given as a distance labeling, that is each vertex receives a label of O(log n) bi...