A tree of order n is said to be graceful if the vertices can be assigned the labels {0,..., n− 1}
such that the absolute value of the differences in vertex labels between adjacent vertices …

A signed graph (or, $ sigraph $ in short) is a graph G in which each edge x carries a value
$\sigma (x)\in\{-,+\} $ called its sign. Given a sigraph S, the negation $\eta (S) $ of the …

A signed graph is a simple graph where each edge receives a sign positive or negative.
Such graphs are mainly used in social sciences where individuals represent vertices friendly …

In this paper, the mathematical problem of automation of encoding a communication/
transportation network is considered for enabling design of appropriate plans for ground …

A (p, q)-graph G=(V, E), that is,| V (G)|= p and| E (G)|= q, is said to be k-hypergraceful if there
exists a decomposition of G into edge induced subgraphs G1, G2,..., Gk having sizes m1 …

A signed graph is a simple graph where each edge receives a sign positive or negative.
Such graphs are mainly used in social sciences where individuals represent vertices friendly …

This chapter is a collection of some basic definitions, literature review of the research topic
which contains definitions and theorems on graphs which are useful for the subsequent …

Abstract In [4], we have proved the necessary condition for sigraphs on union of k copies
cycles of length three with one vertex in common denoted by C k3 to be graceful and …