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All the graphs considered in this article are simple and undirected. Let G = (V(G), E(G)) be a simple undirected Graph. A function f ∶V(G) → {0, 1, 2} is called root cube mean cordial labeling if the induced function f* ∶ E(G) → {0, 1, 2} defined by f * (u) = ⌊ (f (u)) 3 + (f (v)) 3 2 ⌋ satisfies the condition |vf(i) − vf(j)| ≤ 1 and |ef(i) − ef(j)| ≤ 1 for any i,j ∈ {0,1,2} where vf(x) and ef(x) denotes the number of vertices and number of edges with label x respectively and ⌊x⌋ denotes the greatest integer less than or equals to x. A Graph G is called root cube mean cordial if it admits root cube mean cordial labeling. In this article, we have discussed root cube mean cordial labeling of the graph K1,n × Pm. [ABSTRACT FROM AUTHOR]

All the graphs considered in this article are simple and undirected. Let G = (V(G), E(G)) be a simple undirected Graph. A function f ∶ V(G) → {1,2} is called Harmonic Mean Cordial if the induced function f* ∶ E(G) → {1,2} defined by f * (u) = ⌊ (2 f (u) f (v)) (f (u) + f (v)) ⌋ satisfies the condition | vf(i) − vf(j)| ≤ 1 and | ef(i) − ef(j)| ≤ 1 for any i,j ∈ {1,2}, where vf(x) and ef(x) denotes the number of vertices and number of edges with label x respectively and ⌊ x ⌋ denotes the greatest integer less than or equals to x. A Graph is G called Harmonic Mean Cordial graph if it admits Harmonic Mean Cordial labeling. In this article, we have discussed Harmonic Mean Cordial labeling of some interesting graphs. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity which is not a field. The unit graph, U(R) is a simple, undirected graph whose vertex set is the set of all the elements of ring R and two distinct vertices x, y ∊ R are adjacent in U (R) if and only if x + y ∊ U (R); where U (R) denotes the set of all units in R. In this article, we have discussed the complement of the unit graph, (U (R))c. In the first section, we have studied various properties of (U (R))c like diameter, domination number, girth, clique number, planarity, etc. In the second part, we have studied (U (R))c for particular ring R = C(X) = the set of all continuous functions from X to R; where X is a regular T1-space. In this graph, we consider V((U (C(X))c) = the set of all non-constant continuous functions from X to R. [ABSTRACT FROM AUTHOR]

All the graphs considered in this article are simple and undirected. Let G = (V(G), E(G)) be a simple undirected Graph. A function f ∶V(G) → {0, 1, 2} is called root cube mean cordial labeling if the induced function f* ∶ E(G) → {0, 1, 2} defined by f * (u) = ⌊ (f (u)) 3 + (f (v)) 3 2 ⌋ satisfies the condition |vf(i) − vf(j)| ≤ 1 and |ef(i) − ef(j)| ≤ 1 for any i,j ∈ {0,1,2} where vf(x) and ef(x) denotes the number of vertices and number of edges with label x respectively and ⌊x⌋ denotes the greatest integer less than or equals to x. A Graph G is called root cube mean cordial if it admits root cube mean cordial labeling. In this article, we have discussed root cube mean cordial labeling of the graph K1,n × Pm. [ABSTRACT FROM AUTHOR]