# THE VERTEX MONOPHONIC NUMBER OF A GRAPH

## Related Articles

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A subset of vertices of a graph is called a global neighbourhood dominating set(gnd - set) if is a dominating set for both and G and GN, where GNis the neighbourhood graph of G. The global neighbourhood domination number(gnd - number) is the minimum cardinality of a global neighbourhood...

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The article focuses on the classification of antipodal almost distance-transitive graphs of diameter three. It states that a graph is considered as distance-transitive if the group is transitive on the vertex set. It mentions that if vertices were separated by a distance, the graph is called as...

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No abstract available.

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In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P. If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G...

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No abstract available.

- The Number of Independent Sets in a Graph with Small Maximum Degree. Galvin, David; Zhao, Yufei // Graphs & Combinatorics;Mar2011, Vol. 27 Issue 2, p177
Let ind( G) be the number of independent sets in a graph G. We show that if G has maximum degree at most 5 then (where d(ï¿½) is vertex degree, iso( G) is the number of isolated vertices in G and K is the complete bipartite graph with a vertices in one partition class and b in the other),...

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defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set...

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We study the structure of trees minimizing their number of stable sets for given order n and stability number Î±. Our main result is that the edges of a non-trivial extremal tree can be partitioned into n âˆ’ Î± stars, each of size $${\lceil\frac{n-1}{n-\alpha}\rceil}$$ or...

- On Strong(Weak) domination in Fuzzy graphs. Natarajan, C.; Ayyaswamy, S. K. // World Academy of Science, Engineering & Technology;Jul2010, Issue 43, p526
No abstract available.