Journal of the Ramanujan Mathematical Society

J. Paulraj Joseph ¹, S. Arumugam ²

Affiliations
1 Central Prison Palayamkottal - 627 002, IN
2 Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli - 627 009, IN

Abstract

The connected domatic number d_c of a graph G = (V, E) is the maximum order of a partition of V into connected dominating sets in G. In this paper we prove that for any graph G such that both G and G are connected, d_c+d≤p-2 and characterize the class of graphs for which equality holds.

Keywords

Connected Domination, Connected Domatic Number, Perfect Domi Nation.

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N. Veerapandiyah ¹, P. N. Ramachandran ², S. Arumugam ³

Affiliations
1 Department of Mathematics, A.V.V.M. Sri Pushpam College Poondi - Thanjavur -613 503, IN
2 Department of Mathematics A.V.V.M. Sri Pushpam College Poondi, Thanjavur - 613 503, IN
3 Department of Mathematics, St. John's College Palayamkottal - 627 002, IN

Abstract

For a nonnegative integer k, a graph G = (V, E) with | V( G)| > k ( k + 1 ) / 2 is defined to be k - balanced if {| E ( H ) | / (| V ( H) | - k)} ≤ {| E ( G) | / ( | V ( G ) | - k)} for every subgraph H of G with |V ( H) | > k. When k = 0 and 1 this coincides with balanced graphs of Erd6s and Renyi and strongly balanced graphs of Rucinski and Vince, respectively. In this paper we investigate some properties of k - balanced graphs. Given, any two integers p and q with suitable

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