IJPAM: Volume 80, No. 2 (2012)

SOME GRAPH PARAMETERS OF FAN GRAPH

Siriluk Intaja$^1$, Thanin Sitthiwirattham$^2$
$^1$Department of Mathematics
Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok, 10800, THAILAND
$^2$Centre of Excellence in Mathematics, CHE
Sri Ayutthaya Road, Bangkok, 10400, THAILAND


Abstract. The fan graph $F_{m,n} \cong \overline{K}_m \vee P_n,$ is the graph that $V(F_{m,n}) = V(\overline{K}_m) \cup V(P_n)$ and $E(F_{m,n}) = E(P_n) \cup \{uv\vert u \in V(\overline{K}_m),v \in V(P_n)\}.$ Let $\Im$ be a set of all simple graphs. The function $f:\Im\rightarrow Z^+$ is called graph parameter, if $G\cong H,$ then $f(G) = f(H)$. In this paper, we determine generalizations of some graph parameters (clique number, independent number, vertex covering number and domination number) of fan graph.

Received: June 21, 2012

AMS Subject Classification: 05C69, 05C70, 05C76

Key Words and Phrases: joined graph, clique number, independent number, vertex covering number, domination number

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 2