In this paper, we introduce a new labeling called one modulo three harmonic mean labeling. A graph G is said to be one modulo three harmonic mean graph if there is a function φ from the vertex set of G to {1, 3, 4, ... ,3 − 2, 3 } with φ is one-one and φ induces a bijection φ∗ from the edge set of G to {1, 4, ..., 3q 2}, where φ∗(e = uv) = ( ) ( ) ( ) ( ) or ( ) ( ) ( ) ( ) and the function φ i...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...

A proper total-coloring of graph G is said to be equitable if the number of elements (vertices and edges) in any two color classes differ by at most one, which the required minimum number of colors is called the equitable total chromatic number. In this paper, we prove some theorems on equitable total coloring and derive the equitable total chromatic numbers of Pm ∨ Sn, Pm ∨ Fn and Pm ∨Wn. Keyw...

a graph of size n is said to be graceful when is possible toassign distinct integers from {0, 1, . . . , n} to its verticesand {|f(u)−f(v)| : uv ∈ e(g)} consists of n integers. inthis paper we present broader families of graceful graphs; these families are obtained via three different operations: the third power of a caterpillar, the symmetric product of g and k2 , and the disjoint :union: of g...

Problem statement: In this study, we considered an efficient and resilient large file content push problem in a large scale distributed content delivery networks and investigated the Quality of Service (QoS) requirements for content distribution. We investigated the effect of equitable dominating set in SON formation and how it was useful in reducing the redundancy? Approach: At first, we const...

background: definite data regarding the incidence and distribution of renal tumours in eastern india is not known. for better management, as it is essential to identify patients with poor prognosis, prognostic factors like stage, nuclear grade and their relationship to molecular markers are also unclear in this region. the purpose of our study was to assess the spectrum of adult renal tumours w...

A graph that admits a Smarandachely near mean m-labeling is called Smarandachely near m-mean graph. The graph that admits a near mean labeling is called a near mean graph (NMG). In this paper, we proved that the graphs Pn, Cn,K2,n are near mean graphs and Kn(n > 4) and K1,n(n > 4) are not near mean graphs.

Let be a graph. If  , G V E    is a function from the vertex set   V G to the set of positive integers. Then two vertices are   G , u v V   -equitable if     1 u v     . By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equ...