A new algorithm for finding minimum spanning trees with undirected neutrosophic graphs

Abstract

In this paper, we discuss the minimum spanning tree (MST) problem of an undirected neutrosophic weighted connected graph in which a single-valued neutrosophic number, instead of a real number/fuzzy number, is assigned to each arc as its arc length.We define this type of MST as neutrosophic minimum spanning tree (NMST). We describe the utility of neutrosophic numbers as arc lengths and its application in different real world MST problems. Here, a new algorithm for designing the MST of a neutrosophic graph is introduced. In the proposed algorithm, we incorporate the uncertainty in Kruskal algorithm for designing MST using neutrosophic number as arc length. A score function is used to compare different NMSTs whose weights are computed using the addition operation of neutrosophic numbers. We compare this weight of the NMST with that of an equivalent classical MST with real numbers as arc lengths. Compared with the existing algorithms for NMST, the proposed algorithm is more efficient due to the fact that the addition operation and the ranking of neutrosophic number can be done in straightforward manners. The proposed algorithm is illustrated by numerical examples.

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“…In 2018, Broumi et al applied IVNNs and BNS SPP for a given network [70,71]. Dey et al proposed a novel design for MST for NGs which are undirected [78]. Jeyanthi and Radhika [81] solved NSPP using Floyd's algorithm firstly.…”

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“…For more definitions and terminologies, the readers are referred to [30][31][32][33][34][35][36][37][38][39][40][41]. …”

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“…The IVNS [15] is a more general database to generalize the concept of different types of sets to express membership degrees' truth, indeterminacy, and a false degree in terms of intervals. Thus, several papers are published in the field of fuzzy and neutrosophic sets [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62].…”