### Published In

**Volume 4 Issue 3 December-2018**

### Paper Id

**IJIRCT1801011**

### Page Number

**62-67**

### Authors

- V. Viola
- T. Nicholas

### Paper Details

**Title**

# On Radio D-distance Number of Some Basic Graphs

**Abstract**

In this paper we find the radio D-distance number of some standard graphs. If u, v are vertices of a connected graph G, the D-length of a connected u-v path s is defined as l^D(s) = l(s) + deg (v) + deg (u) + Î£ deg(w), where the sum runs over all intermediate vertices w of s and l(s) is the length of the path. The D-distance d^D(u, v) between two vertices u, v of a connected graph G is defined a dá´°(u, v) = min{l^D(s)}, where the minimum is taken over all u-v paths s in G. In other words, dá´°(u, v) = min{l(s) + deg(v) + deg(u) + Î£deg(w)}, where the sum runs over all intermediate vertices w in s and minimum is taken over all u-v paths s in G. Radio D-distance coloring is a function Æ’ : V(G) â†’ N such that d^D(u, v) + |f(u)-f(v)| â‰¥ ã€–diamã€—^D(G) + 1, where ã€–diamã€—^D(G) is the D-distance diameter of G. A D-distance radio coloring number of G is the maximum color assigned to any vertex of G. It is denoted by ã€–rnã€—^D(G).

**Key Words**

D-distance, Radio D-distance coloring, Radio D-distance number.

*. . .*

### Citation

V. Viola, T. Nicholas, "On Radio D-distance Number of Some Basic Graphs", IJIRCT, Volume 4, Issue 3, Pages 62-67, December-2018, https://www.ijirct.org/viewPaper.php?paperId=IJIRCT1801011