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A total edge irregular k-labeling of a graph G = (V, E), ∂: V ∪ E → {1, 2, 3, ⋯, k} is a labeling of vertices and edges of G in such a way that the weights of all edges are distinct. A total edge irregularity strength of graph G, denoted by tes(G) is defined as the minimal k for which a graph G has a totally irregular total k-labeling. Analogously we can define total vertex irregularity strength of graph G, denoted by tvs(G). In this paper, we provide the no-hole total (both edge and vertex) irregularity strength for some well known planar graphs. [ABSTRACT FROM AUTHOR]

A total edge irregular k -labeling of a graph G = (V , E) , ∂ : V ∪ E → { 1 , 2 , 3 , ... , k } is a labeling of vertices and edges of G in such a way that the weights of all edges are distinct. A total edge irregularity strength of graph G , denoted by tes (G) is defined as the minimum k for which a graph G has a totally irregular total k -labeling. In this paper, we define (a , d) -total edge irregularity labeling and provide the irregularity strength for some well-known families of graphs. [ABSTRACT FROM AUTHOR]

An L(2, 1)-labeling of a graph Γ is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let λ12(Γ) denote the least λ such that Γ admits an L(2, 1)-labeling using labels from {0, 1, . . . , λ}. A Cayley graph of group G is called a circulant graph of order n, if G = Zn. In this paper initially we investigate the upper bound for the span of the L(2, 1)-labeling for Cayley graphs on cyclic groups with “large” connection sets. Then we extend our observation and find the span of L(2, 1)-labeling for any circulants of order n.

We introduce Tribonacci cordial labeling as an extension of Fibonacci cordial labeling, a well-known forms of vertex-labelings. A graph that admits Tribonacci cordial labeling is called Tribonacci cordial graph. In this paper we investigate whether some well-known graphs are Tribonacci cordial. [ABSTRACT FROM AUTHOR]

An L (3 , 1) -labeling of a graph Γ is an assignment of non-negative integers to the vertices such that if two vertices u and v are adjacent then they receive labels that differ by at least 3 , and when u and v are not adjacent but there is a two-hop path between them, then they receive labels that differ by at least one. The span λ of such a labeling is the difference between the largest and the smallest vertex labels assigned. Let λ 3 1 (Γ) denote the least λ such that Γ admits an L (3 , 1) -labeling using labels from { 0 , 1 , ... , λ }. A Cayley graph of group G is called circulant graph of order n , if G = ℤ n . In this paper initially we investigate the L (3 , 1) -labeling for circulant graphs with "large" connection sets, and then we extend our observation and find the span of L (3 , 1) -labeling for any circulants of order n. [ABSTRACT FROM AUTHOR]