DOI QR코드

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LINEAR EDGE GEODETIC GRAPHS

  • Santhakumaran, A.P. (Department of Mathematics, St.Xavier's College (Autonomous)) ;
  • Jebaraj, T. (Department of Mathematics, C.S.I. Institute of Technology) ;
  • Ullas Chandran, S.V. (Department of Mathematics, Amrita Vishwa Vidyapeetham University, Amritapuri Campus)
  • 투고 : 2011.09.22
  • 심사 : 2012.01.06
  • 발행 : 2012.09.30

초록

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

키워드

참고문헌

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