# A Characterisation of weak integer additive Set-Indexers of graphs

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Let N0 be the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) of a graph is an injective function âˆ« : V(G)â†’P(N0) such that the induced function âˆ«+ : E(G) â†’P(N0) defined by âˆ«+(uv) = âˆ« (u)+ âˆ« (v) is also...

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A set-labeling of a graph G is an injective function f : V (G) â†’ P(X), where X is a finite set of non-negative integers and a set-indexer of G is a set-labeling such that the induced function fâŠ• : E(G) â†’ P(X) - {Ã˜} defined by fâŠ• (uv) = f(u)?âŠ•(v) for every...

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B.D. Acharya defined an integer additive set indexer (IASI) of a graph G as an injective function f : V(G) â†’ 2N0 such that the induced function gf : E(G) â†’ 2N0 defined by gf (uv) = f(u) + f(v) is also injective, where N0 denotes the set of all nonnegative integers and the notation...

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The colouring number col(G) of a graph G is the smallest integer Îº for which there is an ordering of the vertices of G such that when removing the vertices of G in the specified order no vertex of degree more than Îº -- 1 in the remaining graph is removed at any step. An edge e of a graph G...

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Each polyhedron of full dimension has a unique (up to positive scalar multiples of the inequalities) minimal defining system and a unique minimal totally dual integral defining system with integer left hand sides. These two minimal systems are characterised for the convex hull of the simple...

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This paper derives the set-indexing numbers of certain graphs subsequently identifying some set-semigraceful graphs

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Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: for given m and n with m < n, m is adjacent to n if n has a 1 in the mth position of its binary expansion. It is well known that R is a universal graph in the set...

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A signed graph (or sigraph in short) is an ordered pair S = (Su,Ïƒ), where Su is a graph G = (V, E) and Ïƒ : E â†’{+,-} is a function from the edge set E of Su into the set {+,-}. For a positive integer n, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the...

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Inspired by connections described in a recent paper by Mark L. Lewis, between the common divisor graph G( X) and the prime vertex graph ?( X), for a set X of positive integers, we define the bipartite divisor graph B( X), and show that many of these connections flow naturally from properties of...