Kiki A. Sugeng

( a,d )-edge-antimagic total labelings of caterpillars

For a graph G = (V,E), a bijection g from V(G) ∪ E(G) into { 1,2, ..., ∣ V(G) ∣ + ∣ E(G) ∣ } is called (a,d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a,d)-edge-antimagic total labeling g is called super (a,d)-edge-antimagic total if g(V(G)) = { 1,2,..., ∣ V(G) ∣ } . We study super (a,d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr.

A new approach for determining fuzzy chromatic number of fuzzy graph

A fuzzy graph referred in this paper is a graph with crisp vertex set and fuzzy edge set. The most important issue in the coloring problem of fuzzy graph is to construct a method for finding the chromatic number of fuzzy graph. Most of the methods that many researchers had been done still result crisp chromatic number. In this paper, we propose a new approach to determine fuzzy chromatic set of fuzzy graph. In our proposed method, the fuzzy chromatic set of fuzzy graph is constructed through its δ-chromatic number. Further, we investigate some properties of the fuzzy chromatic set of fuzzy graph. We show that fuzzy chromatic set of fuzzy graph is a discrete fuzzy number and then it is called by fuzzy chromatic number. To the best of our knowledge, no one has determined fuzzy chromatic number of fuzzy graph through its δ-chromatic number before now. Finally, a fuzzy chromatic algorithm based on the new approach is proposed.

An uncertain chromatic number of an uncertain graph based on \alpha -cut coloring

An uncertain graph is a graph in which the edges are indeterminate and the existence of edges are characterized by belief degrees which are uncertain measures. This paper aims to bring graph coloring and uncertainty theory together. A new approach for uncertain graph coloring based on an

Consecutive magic graphs

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Group distance magic and antimagic graphs

α-cut of an uncertain graph is introduced in this paper. Firstly, the concept of

The Construction of Labeling and Total Irregularity Strength of Specified Caterpillar Graph

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