On the minimum degree and edge-connectivity of a graph
Ladislav Nebeský (1976)
Časopis pro pěstování matematiky
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Ladislav Nebeský (1976)
Časopis pro pěstování matematiky
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Jiří Jelínek (2003)
Acta Universitatis Carolinae. Mathematica et Physica
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Amitava Bhattacharya, Gurusamy Rengasamy Vijayakumar (2002)
Discussiones Mathematicae Graph Theory
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Let G be a graph with Δ(G) > 1. It can be shown that the domination number of the graph obtained from G by subdividing every edge exactly once is more than that of G. So, let ξ(G) be the least number of edges such that subdividing each of these edges exactly once results in a graph whose domination number is more than that of G. The parameter ξ(G) is called the subdivision number of G. This notion has been introduced by S. Arumugam and S. Velammal. They have conjectured that for any...
Ladislav Nebeský (1981)
Czechoslovak Mathematical Journal
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Anton Kundrík (1990)
Mathematica Slovaca
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Ladislav Nebeský (2001)
Czechoslovak Mathematical Journal
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By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of...
K.M. Kathiresan, G. Marimuthu, C. Parameswaran (2014)
Discussiones Mathematicae Graph Theory
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In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is...