A Comparative Analysis on Several Crucial Benefits Upon Triangular Sum Graphs: Exploring Triangular Sum Graphs and Their Applications in Graph Theory

Abstract

In this paperwe demonstrate that each tree could be inserted as a triangular sum graph,which may give a stage send in the guess "each tree is a triangular wholediagram" . Additionally we demonstrate that each cycle might be insertedas an incited subgraph of a triangular sum graph, giving some identifiedeffects. We name some groups of triangular sum graphs. Let G = (V,E)be a diagram with p vertices a q edges. A chart G is stated to allow atriangular aggregate naming assuming that its vertices could be named bynon-negative whole numbers such that incited edge marks got by the entirety ofthe names of close vertices are the first q triangular numbers. A chart G whichaffirms a triangular entirety marking is called a triangular entirety chart. Inthe present work we research certain classes of diagrams which does not concedea triangular entirety marking. Likewise we demonstrate that certain classes ofdiagrams might be installed as an impelled subgraph of a triangular sum graph.This work is a decent creation of diagram hypothesis and combinatorial numberhypothesis.