Study of Some Interesting Topics in the Theory of Graphs

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Some Topics of Special Interest in Graph Theory

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Discussion on some interesting topics in Graph Theory

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Discussion On Some Important Topics in Graph Theory

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Some Investigations in the Theory of Graphs

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Sum divisor cordial labeling in the context of graphs operations on bistar

A sum divisor cordial labeling of a graph G with vertex set V (G) is a bijection f : V (G) → {1, 2, 3, . . . , |V (G)|} such that an edge e = uv is assigned the label 1 if2|[f(u)+f(v)] and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph admits a sum divisor cordial labeling, then it is called sum divisor cordial graph. In this paper we prove that bistar Bm,n, splitting graph of bistar Bm,n, degree splitting graph of bistar Bm,n, shadow graph of bistar Bm,n, restricted square graph of bistar Bm,n, barycentric subdivision of bistar Bm,n and corona product of bistar Bm,n with K₁ admit sum divisor cordial labeling.Publisher's Versio

A Creative Review on Coprime (Prime) Graphs

Coprime labelings and Coprime graphs have been of interest since 1980s and got popularized by the Entringer-Tout Tree Conjecture. Around the same time Newman's coprime mapping conjecture was settled by Pomerance and Selfridge. This result was further extended to integers in arithmetic progression. Since then coprime graphs were studied for various combinatorial properties. Here, coprimality of graphs for classes of graphs under the themes: Bipartite with special attention to Acyclicity, Eulerian and Regularity. Extremal graphs under non-coprimality and Eulerian properties are studied. Embeddings of coprime graphs in the general graphs, the maximum coprime graph and the Eulerian coprime graphs are studied as subgraphs and induced subgraphs. The purpose of this review is to assimilate the available works on coprime graphs. The results in the context of these themes are reviewed including embeddings and extremal problems

The Butterflies of Montana with Keys for Determination of Species, 1906

Academic journal published by the University of Montana Biological Station at Flathead Lake.https://scholarworks.umt.edu/umbiologicalseries/1009/thumbnail.jp