Mathematics and Statistics Vol. 10(2), pp. 329 - 334
DOI: 10.13189/ms.2022.100207
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On Tensor Product and Colorability of Graphs

Veninstine Vivik J , Sheeba Merlin G , P. Xavier ^*, Nila Prem JL
Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, India

ABSTRACT

The idea of graph coloring problem (GCP) plays a vital role in allotment of resources resulting in its proper utilization in saving labor, space, time and cost effective, etc. The concept of GCP for graph is assigning minimum number of colors to its nodes such that adjacent nodes are allotted a different color, the smallest of which is known as its chromatic number . This work considers the approach of taking the tensor product between two graphs which emerges as a complex graph and it drives the idea of dealing with complexity. The load balancing on such complex networks is a hefty task. Amidst the various methods in graph theory the coloring is a quite simpler tool to unveil the intricate challenging networks. Further the node coloring helps in classifying the nodes with least number of classes in any network. So coloring is applied to balance the allocations in such complex network. We construct the tensor product between two graphs like path with wheel and helm, cycle with sunlet and closed helm graphs then structured their nature. The coloring is then applied for the nodes of the extended new graph to determine their optimal bounds. Hence we obtain the chromatic number for the tensor product of , , and .

KEYWORDS
Vertex Coloring, Tensor Product, Wheel, Helm, Sunlet

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Veninstine Vivik J , Sheeba Merlin G , P. Xavier , Nila Prem JL , "On Tensor Product and Colorability of Graphs," Mathematics and Statistics, Vol. 10, No. 2, pp. 329 - 334, 2022. DOI: 10.13189/ms.2022.100207.

(b). APA Format:
Veninstine Vivik J , Sheeba Merlin G , P. Xavier , Nila Prem JL (2022). On Tensor Product and Colorability of Graphs. Mathematics and Statistics, 10(2), 329 - 334. DOI: 10.13189/ms.2022.100207.