
Shobna SomasundaramINTI International University | inti · Department of Communication
Shobna Somasundaram
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Publications (28)
Let f:V(G)->{1,2,.....p+q} be an injective function .The induced edge labeling f*(e=uv) is defined by ,f*(e)=[(f(u)^3+f(v)^3)/(f(u)^2+f(v)^2 )] (or) [(f(u)^3+f(v)^3)/(f(u)^2+f(v)^2 )], then f is called Super Lehmer-3 mean labeling, if {f (V(G))} U {f(e)/e ∈ E(G)}={1,2,3,.....p+q}, A graph which admits Super Lehmer-3 Mean labeling is called Super Le...
A graph with vertices and edges is called a Root Square Mean graph if it is possible to label the vertices with distinct elements from in such a way that when each edge is labeled with or , then the resulting edge labels are distinct. In this case is called a Root Square Mean labeling of . The concept of Root Square Mean labeling was introduced by...
A graph G = (V, E) with p vertices and q edges is said to be a mean graph if it is possible to label the vertices x ϵ V with distinct elements f (x) from 0, 1, 2, … , q in such a way that when each edge e = uv is labeled with if f (u) + f (v) is even and if f (u) + f (v) is odd, then the resulting edge labels are distinct. In this case f is called...
A Graph G = (V, E) with p vertices and q edges is said to be a Geometric mean graph if it is possible to label the vertices xϵV with distinct labels f(x) from 1, 2 … … … … q + 1 in such a way that when each edge e = uv is labeled with f (e = uv) = ⌈ f (u) f (v)⌉ or ⌊ f (u) f (v)⌋, then the resulting edge labels are distinct. In this case, f is call...
Let be an injective function. For a vertex labeling f, the induced edge labeling is defined by, or ; then, the edge labels are distinct and are from . Then f is called a root square mean labeling of G. In this paper, we prove root square mean labeling of some degree splitting graphs.
A graph G=(V,E) with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertices x∈V with distinct labels f(x) from 1,2,...,q+1 in such a way that when each edge e=uv is labeled with f(uv)=2f(u)f(v) f(u)+f(v) or 2f(u)f(v) f(u)+f(v) then the edge labels are distinct. In this case f is called harmonic mean labeling...
In this paper we discuss harmonic mean labeling behaviour of some cycle related graphs such as duplication, joint sum of the cycle and identification of cycle. Also we investigate harmonic mean labeling behaviour of alternate triangular snake A(T n ), alternate quadrilateral snake A(Q n ).
A graphs G=(V,E) with p vertices and q edges is said to be a geometric mean graph if it is possible to label the vertices x∈V with distinct labels f(x) from 1, 2,⋯,q+1 in such way that when each edge e=uv is labeled with f(uv)=f(u)f(v) or f(u)f(v) then the edge labels are distinct. Here we prove that C m ∪P n , C m ∪C n , nK 3 ,nK 3 ∪P n , nK 3 ∪C...
In this paper, we obtain necessary and sufficient conditions for the existence of fall coloring with fall achromatic number Δ(G)+1 in the power of a cycle C n k and in the Cartesian product of two cycles.
The index of cordiality of a simple graph G is the min{|e f ' (0)-e f ' (1)|} where the minimum is taken over all the binary labelings of G with |v f (0)-v f (1)|≤1 and f ' (uv)=|f(u)-f(v)|. We obtain upper bounds of this parameter for the union and corona of two graphs with known cordiality indices and also the product of a graph with P 2 . The co...
A graph G=(V, E) with p vertices and q edges is said to be a mean graph if it is possible to label the vertices x?V with distinct elements f (x) from 0, 1, 2, ?, q in such a way that when each edge e=uv is labelled with (f(u)+f(v))/2 if f (u)+f (v) is even and (f (u)+f (v)+1)/2 if f (u)+f (v) is odd, then the resulting edge labels are distinct. f i...
Let G be a graph with vertex set V(G) and edge set E(G). A labeling f:V(G)→4-1,0,1 induces an edge labeling f * defined by f * =f(u)f(v), for each edge uv∈E(G). f is called an EP-cordial labeling if |v f (i)-v f (j)≤1,|e f * (i)-e f * (j)|≤1,i≠j,i,j∈-1,0,1 where v f (x) and e f * ,(x) denote respectively the number of vertices and edges labelled wi...
A bijective labeling on the vertex set V of a simple, finite graph G with labels from {1,2,⋯|V|} called a prime labeling if any two adjacent vertices of G receive co-prime labels. It has been conjectured that ladders are prime. A few cases of ladders have been proved prime in literature and we enlarge this list.
A graph with vertex set V is said to have a prime labeling if its vertices are labelled with distinct integers from {1,2......, |V|}such that for each edge xy, the labels assigned to x and y are relatively prime. A graph that admits a prime labeling is called a prime graph. It has been conjectured [1] that when n is a prime integer and m < n, the p...
In this communication we define degree splitting graph of a graph and we study some properties of degree splitting graph.
We introduce a new type of labeling known as mean labeling. We prove that the following are mean graphs: the path P n , the cycle C n , the complete graph K n for n≤3, the triangular snake and some more special graphs. We also prove that the complete graph K n and the complete bipartite graph K 1,n for n>3 are not mean graphs. From the text: A grap...