Let $G$ be a graph. Let $f:V(G)to{0,1,2, ldots, k-1}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $left|f(u)-f(v)right|$. $f$ is called a $k$-total difference cordial labeling of $G$ if $left|t_{df}(i)-t_{df}(j)right|leq 1$, $i,j in {0,1,2, ldots, k-1}$ where $t_{df}(x)$ denotes the total number of vertices and the edges labeled with $x$.A graph with admits a...

In this paper we introduce remainder cordial labeling of graphs. Let $G$ be a $(p,q)$ graph. Let $f:V(G)rightarrow {1,2,...,p}$ be a $1-1$ map. For each edge $uv$ assign the label $r$ where $r$ is the remainder when $f(u)$ is divided by $f(v)$ or $f(v)$ is divided by $f(u)$ according as $f(u)geq f(v)$ or $f(v)geq f(u)$. The function$f$ is called a remainder cordial labeling of $G$ if $left| e_{...

This book begins with foreword by Prof Mandeep S Dhillon, HOD, Deptt of Orthopedics, PGIMER, Chandigarh in which he has rightly portrayed the role of super-specialty field of neurosurgery in the modern world. But along with that he also explains that because this field is new in India, doctors end up being burdened with the load of work because of scarcity of such super-specialists. And not onl...

Consider a robot that is navigating graph-based space and attempting to determine where it right now. To how distant from each group of fixed landmarks, can send signal. We discuss the problem determining minimum number landmarks necessary their optimal placement ensure always locate itself. The referred as graph's metric dimension, set nodes on which they are distributed known basis. On other ...

vspace{0.2cm} Let $G$ be a graph and $f:V(G)rightarrow {1,2,3,.....left|V(G)right|}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\ $ d_{uv}= begin{cases} left[frac{f(u)}{f(v)}right] ~~if~~ f(u) geq f(v)\ \ left[frac{f(v)}{f(u)}right] ~~if~~ f(v) geq f(u)\ end{cases} $\ for all edge $uv in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{u...

In this paper we generalize the remainder cordial labeling, called $k$-remainder cordial labeling and investigate the $4$-remainder cordial labeling behavior of certain graphs.

Indian music is primarily melodic. Appreciation of it is supposed to be mainly based on the melodic content and rhythm, and not so much on the timbral content. In north Indian classical vocal music (also known as Hindusthani vocal music) raga forms the base bone. The most common style of performance is khayal. The first part in khayal is known as alap, wherein one tries to establish the image a...