The total irregularity strength of m copies of the friendship graph

This paper deals with the totally irregular total labeling of the disjoin union of friendship graphs. The results shows that the disjoin union of  copies of the friendship graph is a totally irregular total graph with the exact values of the total irregularity strength equals to its edge irregular total strength

ON THE IRREGULARITY STRENGTH AND MODULAR IRREGULARITY STRENGTH OF FRIENDSHIP GRAPHS AND ITS DISJOINT UNION

For a simple, undirected graph G with, at most one isolated vertex and no isolated edges, a labeling f:E(G)→{1,2,…,k1} of positive integers to the edges of G is called irregular if the weights of each vertex of G has a different value. The integer k1 is then called the irregularity strength of G. If the number of vertices in G or the order of G is |G|, then the labeling μ:E(G)→{1,2,…,k2}  is called modular irregular if the remainder of the weights of each vertex of G divided by |G| has a different value. The integer k2 is then called the modular irregularity strength of G. The disjoint union of two or more graphs, denoted by ‘+’, is an operation where the vertex and edge set of the result each be the disjoint union of the vertex and edge sets of the given graphs. This study discusses about the irregularity and modular irregularity strength of friendship graphs and some of its disjoint union, The result given is s(Fm ) = m + 1, ms(Fm ) = m + 1 and ms(rFm ) = rm + ⌈r/2⌉, where r denotes the number of copies of friendship graph

NILAI KETAKTERATURAN TOTAL SISI DARI GRAF SEGITIGA BERMUDA

Abstract.For a simple graph G, a labelling λ∶V(G)∪E(G)→ {1,2,…,k} is called an edge irregular total k-labelling of G if for any two different edges e and f of G there is, wt(e)≠wt(f). The total edge irregularity strength denoted by tes G is the smallest positive integer k for which G has an edge irregular total k-labelling. In this paper, we consider the total edge irregularity strength of Bermuda Triangle graph and the union isomorphic and non isomorphic Bermuda Triangle graph. We show that tes(〖Btr〗_(n,4) )= ⌈(30n+17)/3⌉, for n≥1, tes(〖sBtr〗_(n,4) )=⌈(s(30n+15)+ 2)/3⌉, for n≥1 and s≥2, and tes(〖Btr〗_(n,4)∪〖Btr〗_(m,4) )=⌈((30n+15)+ (30m+15)+ 2)/3⌉, for 1≤n≤m. Keywords:Edge irregular total labelling, Irregularity strength, Total edge irregularity strength, Bermuda Triangle graph

On irregularity strength of disjoint union of friendship graphs

<p>We investigate the vertex total and edge total modication of the well-known irregularity strength of graphs. We have determined the exact values of the total vertex irregularity strength and the total edge irregularity strength of a disjoint union of friendship graphs.</p