V. Kamalappan

activity

20172026

collaborators

19 papers

math.CO2026

A study on Type-2 isomorphic circulant graphs. Part 7: Isomorphism series, digraph and graph of $C_{n} (R)$

V. Vilfred Kamalappan

This study is the $7^{t h}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. In this study, we define {\em isomorphic set},…

math.CO2026

A Study on Type-2 Isomorphic Circulant Graphs: Part 8: $C_{432} (R)$ , $C_{6750} (S)$ -- each has 2 types of Type-2 isomorphic circulant graphs

Vilfred Kamalappan

In this study, we obtain the following two families of circulant graphs each has Type-2 isomorphic circulant graphs w.r.t. $m$ such that $m$ has more than one value. (i) Family of…

math.CO2026

A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $&$ -2 isomorphic circulant graphs

Vilfred Kamalappan, Wilson Peraprakash

Elspas and Turner \cite{eltu} raised a question on the isomorphism of $C_{16} (1, 3, 7)$ and $C_{16} (2, 3, 5)$ and Vilfred \cite{v96} gave its answer by defining Type-2 isomorphism of $…

math.CO2026

A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups $(T 2_{n, m} (C_{n} (R)), \circ)$ and $(V_{n, m} (C_{n} (R)), \circ)$

Vilfred Kamalappan

This study is the $6^{t h}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. In this part, we define $V_{n, m} (C_{n} (R))$ and T…

math.CO2026

A study on Type-2 isomorphic circulant graphs. Part 4: 960 triples of Type-2 isomorphic circulant graphs $C_{54} (R)$

Vilfred Kamalappan

This study is the $4^{t h}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10} and is a continuation of Part 3. Here, we study…

math.CO2026

A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96

Vilfred Kamalappan

This study is the $5^{t h}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10} and is a continuation of Part 4. Here, we study…

math.CO2026

A study on Type-2 isomorphic circulant graphs. Part 3: 384 pairs of Type-2 isomorphic circulant graphs $C_{32} (R)$

Vilfred Kamalappan

This study is the $3^{r d}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10} and is a continuation of Part 2. Here, we obtain…

math.CO2026

A study on Type-2 isomorphic circulant graphs. Part 1: Type-2 isomorphic circulant graphs $C_{n} (R)$ w.r.t. $m$ = 2

Vilfred Kamalappan

This study is the first part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. Circulant graphs $C_{n} (R)$ and $C_{n} (S)$ are said to…

math.CO2025

A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27

Vilfred Kamalappan

This study is the $2^{n d}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. Definition of Type-2 isomorphism of circulant g…

math.CO2024

Harary's Sum and Integral Sum Graphs -- A Survey in detail

V. Vilfred Kamalappan, Lowell W. Beineke

Harary introduced the concepts of sum and integral sum graphs. A graph $G$ is a {\em sum graph} if the vertices of $G$ can be labeled with distinct positive integers so that $e = u…

math.CO2023

Constant Sum Partition of ${1, 2, ..., n}$ Into Subsets With Prescribed Orders

V. Vilfred Kamalappan, Sajidha P

Studies on partition of $I_{n}$ = ${1, 2, ..., n}$ into subsets $S_{1}, S_{2}, ..., S_{x}$ so far considered with prescribed sum of the elements in each subset. In this paper, we s…

math.CO2023

Cylindrical Grid Graphs $P_{m} □ C_{n}$ are Non-Distance Magic

Sajidha P, V. Vilfred Kamalappan, Julia K. Abraham

A bijective mapping $f : V (G) \to {1, 2, \dots, n}$ is called a \emph{Distance Magic Labeling (DML) of $G$ } if ~ $\sum_{v \in N (u)} f (v)$ is a constant for all…

math.CO2023

Finding Non-Distance Magic Graphs using neighbourhood chains

V. Vilfred Kamalappan, Sajidha P

Let $G$ be a graph of order $n$ and $N = {N (u_{i})}_{i = 1}^{k}$ be a sequence of neighbourhood(nbh)s in $G$ where $N (u)$ = ${v \in V (G) :$ $uv \in E (G)}$ . \emph{Nbh sequence graph $H…

math.CO2022

$k$ -Distance Magic Labeling and Long Brush Graphs

V. Vilfred Kamalappan

We define a labeling $f :$ $V (G)$ $\to$ ${1, 2, \dots, n}$ on a graph $G$ of order $n \geq 3$ as a \emph{ $k$ -distance magic} ( $k$ -DM) if $\sum_{w\in \partial N_k(u)}{ f(w…

math.CO2022

A study on Type-2 isomorphic circulant graphs. Part 10: Type-2 isomorphic $C_{n p^{3}} (R)$ w.r.t. $m$ = $p$ and related groups

Vilfred Kamalappan, Wilson Peraprakash

This study is the $1 0^{t h}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. In this part, we obtain families of Type-2 iso…

math.CO2022

A study on edge coloring and edge sum coloring of integral sum graphs

V. Vilfred Kamalappan, Lowell W. Beineke, L. Mary Florida +1

Frank Harary introduced the concept of integral sum graph. A graph $G$ is an \emph{ integral sum graph} if its vertices can be labeled with distinct integers so that $e = uv$ is an…

math.CO2020

A study on Type-2 isomorphic circulant graphs and related Abelian groups

V. Vilfred Kamalappan

Circulant graphs $C_{n} (R)$ and $C_{n} (S)$ are said to be \emph{Adam's isomorphic} if there exist some $a \in Z_{n}^{*}$ such that $S = a R$ under arithmetic reflexive modulo $n$ .…

math.GM2019

Generating Prime Numbers -- A Fast New Method

V. Vilfred Kamalappan

Bertrand's Postulate ensures existence of prime $p$ between $n$ and $2 n$ , $n$ an integer $\geq 2$ and the sieve of Eratosthenes, a very simple ancient algorithm, generates all prim…

math.GM2017

The Four Color Theorem -- A New Simple Proof by Induction

V. Vilfred Kamalappan

In 1976, Appel and Haken achieved a major break through by proving the four color theorem $(4 C T)$ . Their proof is based on studying a large number of cases for which a computer-ass…

A study on Type-2 isomorphic circulant graphs. Part 7: Isomorphism series, digraph and graph of Cn​(R)

A Study on Type-2 Isomorphic Circulant Graphs: Part 8: C432​(R), C6750​(S) -- each has 2 types of Type-2 isomorphic circulant graphs

A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 & -2 isomorphic circulant graphs

A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups (T2n,m​(Cn​(R)),∘) and (Vn,m​(Cn​(R)),∘)

A study on Type-2 isomorphic circulant graphs. Part 4: 960 triples of Type-2 isomorphic circulant graphs C54​(R)

A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96

A study on Type-2 isomorphic circulant graphs. Part 3: 384 pairs of Type-2 isomorphic circulant graphs C32​(R)

A study on Type-2 isomorphic circulant graphs. Part 1: Type-2 isomorphic circulant graphs Cn​(R) w.r.t. m = 2

A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27

Harary's Sum and Integral Sum Graphs -- A Survey in detail

Constant Sum Partition of {1,2,...,n} Into Subsets With Prescribed Orders

Cylindrical Grid Graphs Pm​□Cn​ are Non-Distance Magic

Finding Non-Distance Magic Graphs using neighbourhood chains

k-Distance Magic Labeling and Long Brush Graphs

A study on Type-2 isomorphic circulant graphs. Part 10: Type-2 isomorphic Cnp3​(R) w.r.t. m = p and related groups

A study on edge coloring and edge sum coloring of integral sum graphs

A study on Type-2 isomorphic circulant graphs and related Abelian groups

Generating Prime Numbers -- A Fast New Method

The Four Color Theorem -- A New Simple Proof by Induction

A study on Type-2 isomorphic circulant graphs. Part 7: Isomorphism series, digraph and graph of $C_{n} (R)$

A Study on Type-2 Isomorphic Circulant Graphs: Part 8: $C_{432} (R)$ , $C_{6750} (S)$ -- each has 2 types of Type-2 isomorphic circulant graphs

A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $&$ -2 isomorphic circulant graphs

A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups $(T 2_{n, m} (C_{n} (R)), \circ)$ and $(V_{n, m} (C_{n} (R)), \circ)$

A study on Type-2 isomorphic circulant graphs. Part 4: 960 triples of Type-2 isomorphic circulant graphs $C_{54} (R)$

A study on Type-2 isomorphic circulant graphs. Part 3: 384 pairs of Type-2 isomorphic circulant graphs $C_{32} (R)$

A study on Type-2 isomorphic circulant graphs. Part 1: Type-2 isomorphic circulant graphs $C_{n} (R)$ w.r.t. $m$ = 2

Constant Sum Partition of ${1, 2, ..., n}$ Into Subsets With Prescribed Orders

Cylindrical Grid Graphs $P_{m} □ C_{n}$ are Non-Distance Magic

$k$ -Distance Magic Labeling and Long Brush Graphs

A study on Type-2 isomorphic circulant graphs. Part 10: Type-2 isomorphic $C_{n p^{3}} (R)$ w.r.t. $m$ = $p$ and related groups