Some New Graceful Generalized Classes of Diameter Six Trees

Here we denote a {\it diameter six tree} by $(c; a_{1}, a_{2}, \ldots, a_{m}; b_{1}, b_{2}, \ldots, b_{n}; c_{1}, c_{2}, \ldots, c_{r})$, where $c$ is the center of the tree; $a_{i}, i = 1, 2, \ldots, m$, $b_{j}, j = 1, 2, \ldots, n$, and $c_{k}, k = 1, 2, \ldots, r$ are the vertices of the tree adjacent to $c$; each $a_{i}$ is the center of a diameter four tree, each $b_{j}$ is the center of a star, and each $c_{k}$ is a pendant vertex. Here we give graceful labelings to some new classes of diameter six trees $(c; a_{1}, a_{2}, \ldots, a_{m}; b_{1}, b_{2}, \ldots, b_{n}; c_{1}, c_{2}, \ldots, c_{r})$ in which a diameter four tree may contain any combination of branches with the total number of branches odd though with some conditions on the number of odd, even, and pendant branches. Here by a branch we mean a star, i.e. we call a star an odd branch if its center has an odd degree, an even branch if its center has an even degree, and a pendant branch if it is a pendant vertex

Abstracts of National Conference on Research and Developments in Material Processing, Modelling and Characterization 2020

This book presents the abstracts of the papers presented to the Online National Conference on Research and Developments in Material Processing, Modelling and Characterization 2020 (RDMPMC-2020) held on 26th and 27th August 2020 organized by the Department of Metallurgical and Materials Science in Association with the Department of Production and Industrial Engineering, National Institute of Technology Jamshedpur, Jharkhand, India. Conference Title: National Conference on Research and Developments in Material Processing, Modelling and Characterization 2020Conference Acronym: RDMPMC-2020Conference Date: 26–27 August 2020Conference Location: Online (Virtual Mode)Conference Organizer: Department of Metallurgical and Materials Engineering, National Institute of Technology JamshedpurCo-organizer: Department of Production and Industrial Engineering, National Institute of Technology Jamshedpur, Jharkhand, IndiaConference Sponsor: TEQIP-