We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.

We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.

In this paper we introduce remainder cordial labeling of graphs. Let G be a (p, q) graph. Let f : V (G)→ {1, 2, ..., p} be a 1-1 map. For each edge uv assign the label r where r is the remainder when f(u) is divided by f(v) or f(v) is divided by f(u) according as f(u) ≥ f(v) or f(v) ≥ f(u). The function f is called a remainder cordial labeling of G if |ef (0) - ef (1)| ≤ 1 where ef(0) and ef(1) respectively denote the number of edges labeled with even integers and odd integers. A graph G with a remainder cordial labeling is called a remainder cordial graph. We investigate the remainder cordial behavior of path, cycle, star, bistar, crown, comb, wheel, complete bipartite K2,n graph. Finally we propose a conjecture on complete graph Kn.