Maximum Degree Based Vertex Graceful Labeling Graph With Odd Labeling on Edges K. Thiagarajan, V. Rajeswari and Ponnammal Natarajan Abstract We described and studied the concept of maximum degree based ver- tex graceful labeling graph with odd labeling on edges in this approach. It is a particular type of labeling vertex of a graph G with p vertices and q edges if there exists a bijection f from the edge set to the set {1, 3, 5,...,(2q - 1)} so that the induced mapping f * : V →{0, 1, 2,...,(2q - 1)} which is given by f * (u ) =  ∑ f (uv)   /u v ∈ E (G)  , where  is maximum degree of G, [] denotes the integral part. Keywords Crown graph · Degree · Edge · Maximum · Odd · Vertex 1 Introduction Graph labeling [1–3] is an assignment of integers to the vertices or edges or both subject to certain conditions. Graph labeling is extremely useful in various areas such as coding theory, mobile, optimal circuits’ layout, graph decomposition problems, communication networks, and designing. Nowadays, graph labeling is fascinated by researchers to work on it. K. Thiagarajan (B ) Academic Research, Jeppiaar Engineering College, Chennai, Tamilnadu, India e-mail: vidhyamannan@yahoo.com V. Rajeswari Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, Tamilnadu, India e-mail: joynaren7802@gmail.com Ponnammal Natarajan Department of Mathematics, Anna University, Chennai, Tamil Nadu, India e-mail: pamman01@yahoo.com © Springer Nature Singapore Pte Ltd. 2020 S. C. Satapathy et al. (eds.), Smart Intelligent Computing and Applications, Smart Innovation, Systems and Technologies 159, https://doi.org/10.1007/978-981-13-9282-5_26 287