Abstract:
The concept of cordial labeling in graphs motivated us to introduce cordial words, cordial languages and cordial numbers. We interpret the notion of cordial labeling in Automata and thereby study the corresponding languages. In this paper we develop a new sequence of numbers called the cordial numbers in number theory using the labeling techniques in graph theory on automata theory.

Abstract:
We introduce two new measures of the noncordiality of a graph. We then calculate the values of these measures for various families of noncordial graphs. We also determine exactly which of the M\"obius ladders are cordial.

Abstract:
We calculate the cordial edge deficiencies of the complete multipartite graphs and find an upper bound for their cordial vertex deficiencies. We also give conditions under which the tensor product of two cordial graphs is cordial.

Abstract:
Let f be a map from V(G) to . For each edge uv assign the label . f is called a mean cordial la- beling if and , , where and denote the number of vertices and edges respectively labelled with x ( ). A graph with a mean cordial labeling is called a mean cor- dial graph. We investigate mean cordial labeling behavior of Paths, Cycles, Stars, Complete graphs, Combs and some more standard graphs.

Abstract:
In this paper we prove that the split graphs of K_{1,n } and B_{n,n} are prime cordial graphs. We also show that the square graph of B_{n,n} is a prime cordial graph while middle graph of P_{n} is a prime cordial graph for n≥4 . Further we prove that the wheel graph W_{n} admits prime cordial labeling for n≥8.

Abstract:
A new concept of labeling called the signed product cordial labeling is introduced and investigated for path graph, cycle graphs, star-K_{1,n}, Bistar-B_{n,n}, and Some general results on signed product cordial labeling are studied.

Abstract:
A binary vertex labeling of graph $ G $ with induced edge labeling $ f^{*}:E(G) ightarrow {0,1} $ defined by $ f^{*}(e=uv)=f(u)f(v) $ is called a extit{product cordial labeling} if $ vert v_{f}(0) - v_{f}(1) vert leq 1 $ and $ vert e_{f}(0) - e_{f}(1) vert leq 1 $. A graph is called extit{product cordial} if it admits product cordial labeling. We prove that the shell admits a product cordial labeling. Sundaram et al.cite{Sundaram1} proved that if a graph with $p$ vertices and $ q$ edges with $ p geq 4 $ is product cordial then $ q leq dfrac{p^{2}-1}{4} + 1 $. We present here some families of graphs which satisfy this condition but not product cordial.

Abstract:
Let $G=(V,E)$ be a $(p,q)$-graph. A Fibonacci divisor cordial labeling of a graph G with vertex setV is a bijection $f : V ightarrow {F_1, F_2,F_3,dots ,F_p}$, where$F_i$ is the $i^{th}$ Fibonacci number such that if each edge $uv$ is assigned the label $1$ if $f(u)$ divides $f(v)$ or $f(v)$ divides $f(u)$ and $0$ otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a Fibonacci divisor cordial labeling, then it is called Fibonacci divisor cordial graph. In this paper, we prove that the graphs $P_n$, $C_n$, $K_{2,n} odot u_2(K_1)$ and subdivision of bistar( extless $B_ {n,n}:w>)$ are Fibonacci divisor cordial graphs. We also prove that $K_n(ngeq 3)$ is not Fibonacci divisor cordialgraph.

Abstract:
Hovey introduced a $k$-cordial labeling of graphs as a generalization both of harmonious and cordial labelings. He proved that all tress are $k$-cordial for $k \in \{1,...,5\}$ and he conjectured that all trees are $k$-cordial for all $k$. \indent We consider a corresponding problem for hypergraphs, namely, we show that $p$-uniform hypertrees are $k$-cordial for certain values of $k$.