An injective function f : V pGq Ñ t0, 1, 2, . . . , qu is an odd sum labeling if the induced edge labeling f defined by f puvq fpuq fpvq, for all uv P EpGq, is bijective and f pEpGqq t1, 3, 5, . . . , 2q 1u. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper we study the odd sum property of graphs obtained by duplicating any edge of some graphs.

The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In [6] Hanyuan Deng et.al computed indices four new operations on a graph defined by M. Eliasi, B. Taeri [4]. Motivated from this we define operation graphs compute resultant graph. We illustrate results with some examples.

We introduce and analyse a new class of graphs called SM-sum graphs. This has been done by using the concept that any positive integer can be expressed as a sum of powers of 2. This relation between powers of 2 and other positive integers are very much used in Computer Science especially in the binary number system, bit string operations, in signal processing etc. We are making use of this rela...

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...

Let G be a graph. Assume that l and k are two natural numbers. An l-sum flow on a graph G is an assignment of non-zero real numbers to the edges of G such that for every vertex v of G the sum of values of all edges incident with v equals l. An l-sum k-flow is an l-sum flow with values from the set {±1, . . . ,±(k − 1)}. Recently, it was proved that for every r, r > 3, r 6= 5, every r-regular gr...

A theta graph Θ2,1,2 is a obtained by joining two vertices three internally disjoint paths of lengths 2, 1, and 2. neighbor sum distinguishing (NSD) total coloring ϕ G proper such that ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each edge uv∈E(G), where EG(u) denotes the set edges incident with vertex u. In 2015, Pilśniak Woźniak introduced this conjectured every maximum degree Δ admits an NSD (Δ+3)-...