Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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Let G be a connected graph and k be an integer, k ≥ 1. If l: V (G) → N is a vertex labΣeling of a graph G, then e-lucky sum of a vertex u ∈ V (G) is el(u) Σv∈N (u) l(v) + e(u), where e(u) denotes the eccentricity of u and N (u) denotes the open neighborhood of u. The labeling is e-lucky labeling if el(u) ƒ= el(v), for every uv ∈ E(G). The e-lucky number ηel(G) of G is the smallest integer k for which G has e-lucky labeling. In this paper, we compute the e-lucky number for book graph, butterfly network and complete graph. Also, we give the sharp bound for any regular bipartite self-centered graphs. © 2020. All rights reserved

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Department of Mathematics

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Vellore Campus

International Journal of Mathematics and Computer Science

e-Lucky Labeling of Certain Graphs

The packing chromatic number Xρ(G) of a connected graph G is the smallest number m for which a function g:V(G) → {1,2,…,m} exists, such that if g(a)=g(b)=j, then d(a,b)&gt;j. Here, we determine the packing chromatic numbers of bismuth tri-iodide and first type nanostar dendrimers. © 2019, Gazi University Eti Mahallesi. All Rights Reserved.

Gazi University Journal of Science

Packing chromatic number of bismuth tri-iodide and first type nanostar dendrimers

Binary trees are enormously used in data structure as they can be easily stored, manipulated, and retrieved. The most straightforward and extensive applications of binary trees are in the study of computer searching and sorting methods, binary identification problems, and variable binary codes. Many complex networks are easily classified and analyzed by the usage of binary tree representations. A binary tree is defined as a tree in which there is exactly one vertex of degree two and each of the remaining vertices is of degree one or three. Every binary tree is a rooted tree with odd number of vertices. A special type of binary tree known as hypertree is an interconnection topology which combines the easy expansibility of tree structures with the compactness of the hypercube. In this paper we find the Wiener index of hypertree. © Springer Nature Switzerland AG 2019.

Trends in Mathematics

Wiener index of hypertree

The packing chromatic number χρ(G) of a graph G is the smallest integer k for which there exists a mapping π:V(G)⟶{1,2,…,k} such that any two vertices of color i are at distance at least i+1. In this paper, we compute the packing chromatic number for certain fan and wheel related graphs. © 2016 Kalasalingam University

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AKCE International Journal of Graphs and Combinatorics

Packing chromatic number of certain fan and wheel related graphs

Given an undirected 2-edge connected graph, finding a minimum 2-edge connected spanning subgraph is NP-hard. We solve the problem for Butterfly network, Benes network, Honeycomb network and Sierpiński gasket graph.

Journal of Combinatorial Mathematics and Combinatorial Computing

Minimum 2-edge connected spanning subgraph of certain graphs

The packing chromatic number Xp(G) of a graph G is the smallest integer k for which there exists a mapping II : V (G) → {1, 2, ⋯, k} such that any two vertices of color i are at distance at least i + 1. It is a frequency assignment problem used in wireless networks, which is also called broadcasting coloring. It is proved that packing coloring is NP-complete for general graphs and even for trees. In this paper, we study the packing chromatic number of comb graph, circular ladder, windmill, H-graph and uniform theta graph. © 2013 Academic Publications, Ltd.